Library Guides: Trigonometry: Coterminal Angles

Coterminal Angles

Coterminal angles are angles in standard position (angles with the initial side on the positive $x$ -axis) that have a common terminal side. For example, $- 330 °$ and $390 °$ are all coterminal.

To find a positive and a negative angle coterminal with a given angle, you can add and subtract $360 °$ if the angle is measured in degrees or $2 π$ if the angle is measured in radians.

Example 1:

Find a positive and a negative angle coterminal with a $55 °$ angle.

$\begin{array}{l} 55 ° - 360 ° = - 305 ° \\ 55 ° + 360 ° = 415 ° \end{array}$

A $- 305 °$ angle and a $415 °$ angle are coterminal with a $55 °$ angle.

Example 2:

Find a positive and a negative angle coterminal with a $\frac{π}{3}$ angle.

$\begin{array}{l} \frac{π}{3} + 2 π = \frac{7 π}{3} \\ \frac{π}{3} - 2 π = - \frac{5 π}{3} \end{array}$

A $\frac{7 π}{3}$ angle and a $- \frac{5 π}{3}$ angle are coterminal with a $\frac{π}{3}$ angle.

Reference - https://www.varsitytutors.com/hotmath/hotmath_help/topics/coterminal-angles

Find four coterminal angles of the following: Draw the coterminal angle with the original angle

210º

-72º

510º

Key questions to consider:

Have you tried finding coterminal angles in both positive and negative directions?

What is the same between the coterminal and original angles?

What is different between the coterminal and original angles?

How many times coterminal angles are possible?

What applications can you use coterminal angles? For example, think of car tire rotating more than one time around.