Pre-Calculus - Angles in the Coordinate Plane

Find the coterminal angle of 15 degrees.

$\textup{All of the answers represent coterminal angles.}$

$-705^{\circ}$

$375^{\circ}$

$735^{\circ}$

$-345^{\circ}$

Explanation

The coterminal angles can be positive or negative. To find the coterminal angles, simply add or subtract 360 degrees as many times as needed from the reference angle.

All of these angles are coterminal angles.

Find the coterminal angle of 15 degrees.

$\textup{All of the answers represent coterminal angles.}$

$-705^{\circ}$

$375^{\circ}$

$735^{\circ}$

$-345^{\circ}$

Explanation

The coterminal angles can be positive or negative. To find the coterminal angles, simply add or subtract 360 degrees as many times as needed from the reference angle.

All of these angles are coterminal angles.

Of the given answers, what of the following is a coterminal angle of $\pi$ radians?

$3\pi$

$2\pi$

$\frac{\pi}{2}$

$\frac{3\pi}{2}$

$-2\pi$

Explanation

To find the coterminal angle of an angle, simply add or subtract $2\pi$ radians, or 360 degrees as many times as needed.

$\pi+2\pi=3\pi$

$\pi-2\pi=-\pi$

$3\pi+2\pi=5\pi$

$-\pi-2\pi=-3\pi$

These are all coterminal angles to $\pi$ radians.

Out of the given answers, $3\pi$ is the only possible answer.

Of the given answers, what of the following is a coterminal angle of $\pi$ radians?

$3\pi$

$2\pi$

$\frac{\pi}{2}$

$\frac{3\pi}{2}$

$-2\pi$

Explanation

To find the coterminal angle of an angle, simply add or subtract $2\pi$ radians, or 360 degrees as many times as needed.

$\pi+2\pi=3\pi$

$\pi-2\pi=-\pi$

$3\pi+2\pi=5\pi$

$-\pi-2\pi=-3\pi$

These are all coterminal angles to $\pi$ radians.

Out of the given answers, $3\pi$ is the only possible answer.

Find the degree measure of $\frac{11}{8} \pi$ radians. Round to the nearest integer.

Explanation

In order to solve for the degree measure from radians, replace the $\pi$ radians with 180 degrees.

$\pi \textup{ radians} = 180 \textup{ degrees}$

$\frac{11}{8} (180) = \frac{11\times 45}{2} = \frac{495}{2}= 247.5$

The nearest degree is .

Find the degree measure of $\frac{11}{8} \pi$ radians. Round to the nearest integer.

Explanation

In order to solve for the degree measure from radians, replace the $\pi$ radians with 180 degrees.

$\pi \textup{ radians} = 180 \textup{ degrees}$

$\frac{11}{8} (180) = \frac{11\times 45}{2} = \frac{495}{2}= 247.5$

The nearest degree is .

Find the coterminal angle of $10^\circ$ , if possible.

$-350^\circ$

$350^\circ$

$\textup{The coterminal angle does not exist.}$

$190^\circ$

$-190^\circ$

Explanation

In order to find a coterminal angle, or angles of the given angle, simply add or subtract 360 degrees of the terminal angle as many times as possible.

The only correct answer is .

Find the coterminal angle of $10^\circ$ , if possible.

$-350^\circ$

$350^\circ$

$\textup{The coterminal angle does not exist.}$

$190^\circ$

$-190^\circ$

Explanation

In order to find a coterminal angle, or angles of the given angle, simply add or subtract 360 degrees of the terminal angle as many times as possible.

The only correct answer is .

Find the coterminal angle of 15 degrees in standard position from the following answers.

$-705^{\circ}$