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.