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14.2 Unit Circle Notes Date: Recall: Reciprocals of sine, cosine, and tangent
Reciprocal of sine:
Reciprocal of cosine: Reciprocal of tangent:
Unit circle: circle with radius 1 unit For every point on the unit circle, we can draw a right triangle: Using Right Triangle Trig, write down the following in terms of x and y:
sinT ____ cscT _____ cosT ____ secT _____ tanT ____ cotT _____ Therefore (x,y) =
Terminal Side on an Axis Assume this is a unit circle. Find sin, cos, tan.
Deg: Rad:
sin𝜃:
cos 𝜃:
tan 𝜃:
How to remember SIGNS of ALL trig ratios: ALL STUDENTS TAKE CALCULUS
You can use reference angles and special right triangles for trig ratios of angles that are not in Quadrant I.
Special Right Triangles:
Deg: Rad:
sin𝜃:
cos 𝜃:
tan 𝜃:
Find exact trig value using reference angle
sin−25𝜋6
Positive:
sin, csc
Positive:
tan, cot
Positive:
All
Positive:
cos, sec
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Kuta Software - Infinite Algebra 2 Name___________________________________
Period____Date________________Exact Trig Values of Special Angles
Find the exact value of each trigonometric function.
1) tan
θ
x
y
60°
3
2) sin
θ
x
y
225°
−
2
2
3) sin
θ
x
y
90°
1
4) cos
θ
x
y
150°
−
3
2
5) cos
θ
x
y
90°
0
6) tan
θ
x
y
240°
3
7) cos
θ
x
y
135°
−
2
28) tan
θ
x
y
150°
−
3
3
-1-
Unitcirdews 'sANSKEYWHNH
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9) cos
θ
x
y
270°
0
10) tan
θ
x
y
225°
1
11) cos 270°
0
12) sin 0
0
13) cot
7
π
4
−1
14) csc
2
π
3
2 3
3
15) csc 225°
− 2
16) sin 300°
−
3
2
17) csc 90°
1
18) tan 240°
3
19) sin
π
4
2
2
20) tan 120°
− 3
21) tan
−13
π
6
−
3
3
22) cos −630° 0
23) cos 990° 024) csc
−31
π
62
25) csc
−5
π
6−2 26) cos
−17
π
3
1
2
27) sin
29
π
6
1
2
28) sec 945°
− 2
29) cos
−11
π
2
0
30) sin −2
π
0
-2-
Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware.com
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Unit Circle Worksheet C Name___________________ Period___________ The given point P is located on the Unit Circle. State the quadrant and find the angle , also sin , cos and tan .
1) 1 3,2 2
P 2) (0, 1)P 3) 2 2,2 2
P
Quad: Quad: Quad: sin : sin : sin :
cos : cos : cos : tan : tan : tan : Find the exact value of each function.
4) 7cos4
5) sin 30D 6) 2sin3
7) cos(600 )D 8) 9sin2
9) tan(7 )
10) 11cos4
11) sin 225D 12) tan(585 )D
13) cos(1440 )D 14) 13sin4
15) 23cos6
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