Coterminal Angles

What are coterminal angles?

• Two angles in standard position that have the same terminal side are called coterminal.

Initial side

Terminal side

Y

X

STANDARD POSITION

How do you find a coterminal angle?

• To find a coterminal angle, you add or subtract multiples of a complete revolution (360o)

• Remember one revolution in radians is 2 π

• 2 π = 360o

To find the smallest positive coterminal angle for:

• 832o

• 832 – 360 = 472, 472 – 360 = 112

• Since we can not subtract another 360o without getting a negative answer, we say that 112o is the smallest positive coterminal angle for 832o

To find the smallest positive coterminal angle for:

•

• + = + =

• Since we do not need to add another

to get a positive answer, we say that is

the smallest positive coterminal angle for

4

3

4

3 2 4

34

84

5

24

5

4

3

To find the smallest positive coterminal angle for:

• 1)

• 2) -570o

3

5