Trigonometric Ratios of Special Angles
Transcript of Trigonometric Ratios of Special Angles
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Trigonometric Ratios ofQuadrantal Angles
90
270
How do we find trig values in this case?
90
180
270
360
90
180
270
360
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Recall:
y
x
y
x
r
P(x, y)
Let P(x, y) be a pointon the terminal sideof angle .
sin = yr cos = x
r tan = y
x
csc =r
y
sec =r
x
cot =x
y
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Consider a unit circle
sin 90=
= 1
cos 90=x
r= 0
tan 90= yx
=
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Consider a unit circle
sin 180=
= 0
cos 180=x
r= 1
tan 180= yx
= 0
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Consider a unit circle
sin 270=
= 1
cos 270=x
r= 0
tan 270= yx
=
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Consider a unit circle
sin 360=
= 0
cos 360=x
r= 1
tan 360= yx
= 0
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Summary
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Consider an equilateral triangle.
Divide the triangle into 2 equal right angledtriangles.
60
60
60
22
2
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60
60
30
1
22
2
Consider just one ofthe triangles.
60
30
1
2
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1
2
3
60sin
2
3
60cos
60tan
2
13
30sin
30cos
30tan
2
3
2
1
3
1
312 22
60
30
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1
1
45
45
211
22
2
45cos45sin
45tan2
11
Let the equal sides have
length 1.
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Trigonometric Ratio of
Special Angles
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Unit Circle
30
1
2
3
2
1
3
2,1
2
http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971 -
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Unit Circle
45
2
2
2
2
1
2
2,
2
2
http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971 -
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Unit Circle
601
2
3
2
1
1
2,
3
2
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8/10/2019 Trigonometric Ratios of Special Angles
17/28
Unit Circle1
2
,3
2
3
2,1
2
2
2,
2
2
sin 30 =1
2
cos 30 =3
2
tan 30 =3
3
csc 30 = 2
sec 30 =2 3
3
cot 30 = 3
http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971 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8/10/2019 Trigonometric Ratios of Special Angles
18/28
Unit Circle1
2
,3
2
3
2,1
2
2
2,
2
2
sin 45 =2
2
cos 45 =2
2
tan 45 = 1
csc 45 = 2
sec 45 = 2
cot 45 = 1
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8/10/2019 Trigonometric Ratios of Special Angles
19/28
Unit Circle1
2
,3
2
3
2,1
2
2
2,
2
2
sin 60 =3
2
cos 60 =1
2
tan 60 = 3
csc 60 =2 3
3
sec 60 = 2
cot 60 =3
3
http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971 -
8/10/2019 Trigonometric Ratios of Special Angles
20/28
In general,
sin = cos =
tan =
csc =1
sec =
1
cot =
http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971 -
8/10/2019 Trigonometric Ratios of Special Angles
21/28
Unit Circle 0,1
1,0
0,1
1,0 sin 90 = 1
cos 90 = 0
tan 90 =
csc 90 = 1
sec 90 =
cot 90 = 0
http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971 -
8/10/2019 Trigonometric Ratios of Special Angles
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Unit Circle 0,1
sin 180 = 0
cos 180 = 1
tan 180 = 0
1,0
0,1
1,0
csc 180 =
sec 180 = 1
cot 180 =
http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971 -
8/10/2019 Trigonometric Ratios of Special Angles
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Unit Circle 0,1
1,0
0,1
1,0 sin 270 = 1
cos 270 = 0
tan 270
= csc 270 = 1
sec 270 =
cot 270 = 0
http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971 -
8/10/2019 Trigonometric Ratios of Special Angles
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Unit Circle 0,1
sin 360 = 0
cos 360 = 1
tan 360 = 0
1,0
0,1
1,0
csc 360 =
sec 360 = 1
cot 360 =
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Degrees
0
30
45
60
90
120
135
150
180
210
245
270300
315
345
360
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Example 1: Find sin 225
Get the quadrant:
III -> Cast rule -> sine is (-)Get the reference angle :
45
sin 45= 2/2
sin 225= -2/2
Determining the trig ratio from thespecial triangles or fingers
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Example 2: Find tan 120
Get the quadrant:
II -> Cast rule ->tangent is (-)
Get the reference angle :
60->Using fingers or special triangles, we
determine tan 60= 3
tan 120=
-3
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Seatwork:
Page 197 (workbook)