Coterminal Angles | find coterminal angle

Two angles are coterminal angle if they are drawn in the standard position and both have their terminal sides in the same location, To find negative and positive coterminal Angles with a given angle, you can subtract and add 360° if the angle is given in degrees or 2π if the angle is given in radians.See below diagram of Coterminal Angles, in which given angle 60° and Coterminal Angles of 60° is (60°-360°) and (360°+60°), negtive and positive coterminal respectivly.
Angles that are coterminal have the same value for function like sin, cos, tan, 60°, 420° and -300° are coterminal, and so sin60°, sin420° and sin(-300°) all have the same value(√3/2).
Fig: Coterminal Angles 

Examples of Coterminal Angles
Q.1 Find a positive and a negative angle coterminal with a 65° angle?
Ans. 65°−360°=−295° and 65°+360°=425°, −295° angle and a 425° angle are coterminal with a 65° angle. 
Q.2 Find a positive and a negative angle coterminal with a 45° angle?
Ans. 45°−360°=−315° and 45°+360°=405°, −315° angle and a 405° angle are coterminal with a 45° angle.
Q.3 Find a positive and a negative angle coterminal with a 95° angle?
Ans. 95°−360°=−265° and 65°+360°=455°, −265° angle and a 455° angle are coterminal with a 95° angle. 
Q.4 Find a positive and a negative angle coterminal with a 15° angle?
Ans. 15°−360°=−345° and 15°+360°=475°, −345° angle and a 475° angle are coterminal with a 15° angle.
Q.5 Find a positive and a negative angle coterminal with a 90° angle?
Ans. 90°−360°=−270° and 90°+360°=450°, −270° angle and a 450° angle are coterminal with a 90° angle. 
Q.6 Find a positive and a negative angle coterminal with a 30° angle?
Ans. 30°−360°=−330° and 30°+360°=390°, −330° angle and a 390° angle are coterminal with a 30° angle.

Related Posts