# How do you find the coterminal with the angle 30^circ?

Aug 8, 2017

Add or subtract any whole number multiple of ${360}^{\circ}$.

#### Explanation:

We con go all the way around the circle in either diection and and up on the positive $x$ axis. If we then go ${30}^{\circ}$ more, we get an angle that is coterminal with ${30}^{\circ}$.

${360}^{\circ} + {30}^{\circ} = {390}^{\circ}$ is coterminal with ${30}^{\circ}$.

$2 \times {360}^{\circ} + {30}^{\circ} = {780}^{\circ} + {30}^{\circ} = {810}^{\circ}$ is coterminal with ${30}^{\circ}$.

$10 \times {360}^{\circ} + {30}^{\circ} = {3600}^{\circ} + {30}^{\circ} = {3630}^{\circ}$ is coterminal with ${30}^{\circ}$.

$- {360}^{\circ} + {30}^{\circ} = - {330}^{\circ}$ is coterminal with ${30}^{\circ}$.

$4 \times - {360}^{\circ} + {30}^{\circ} = - {1440}^{\circ} + {30}^{\circ} = - {1410}^{\circ}$ is coterminal with ${30}^{\circ}$.