State both a positive and negative coterminal angle for each

State both a positive and negative co-terminal angle for each given angle measure.

1. 165°

2. -225°

3. 585°

Solution

1) 165 degrees

positive coterminal angle is

360 + 165 = 525 degrees

negative co terminal angle is

165 - 360 = - 195 degrees

2) - 225 degrees

positive coterminal angle is

360 - 225 = 135 degrees

negetive coterminal angle is

-225 - 360 = - 585 degrees

3) 585 degrees

positive coterminal angle is

585 - 360 = 225 degrees

negative coterminal angle is

585 - 2* 360 = - 135 degrees