initial side: is always the positive x-axis
terminal side
Positive angles are measured counterclockwise.Negative angles are measured clockwise.
0°, 360°-360°
270°-90°
180°-180°
90°-270°
Coterminal AnglesWe can have infinitely many positive AND
negative coterminal angles.
For degrees, add 360° for positive coterminal angles, subtract 360° for negative coterminal angles.
Example: Find a negative coterminal angle for 423°.
answer: -297°
Converting• To convert from degrees to radians:
multiply by 180
rad
140 7140
180 180 9
radrad
• To convert from radians to degrees: multiply by
180rad
• Example: Convert to radians
140
Reference Angles1. Sketch the angle
2. Draw a line from the terminal side to the X-Axis (never to y-axis) to create a right triangle
3. Subtract to find size of reference angle, answer is always positive and between 0° and 90°.
Example: Find the reference angle for 213
213180 213 180 33
33
Trig Functions – Right Triangles
hypotenuse (hyp)
Identifying the legs is relative to the angle
adjacent (adj)
opposite(opp)
hypotenuse (hyp)
adjacent (adj)
opposite(opp)
hyp
oppsin
hyp
adjcos
adj
opptan
SOH-CAH-TOA
cos :
sin :
tan :
cos :
sin :
tan :
cos :
sin :
tan :
cos :
sin :
tan :
How to remember which are positive where:All Spiders Taste CrunchyA: allS: sinT: tanC: cos
allsin
tan cos
Trig FunctionsLet (-5, 12) be a point on the terminal side of an angle in
standard position. Find the value for sin , cos , and tan
12sin
13
5cos
13
5tan
12
First, sketch the point.
.
Second, create a right triangle always using the x-axis forone of the legs.
Third, label the legs and find the hypotenuse.
12
5
2 2 2
2
2
5 12
25 144
169
13
h
h
h
h
13Find the value for the trig functionspaying attention tothe quadrant the point is in.
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