Find the Measure of a Coterminal Angle

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Pre-Calculus › Find the Measure of a Coterminal Angle

Questions 1 - 6
1

Find the coterminal angle of 15 degrees.

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.

2

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

Explanation

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

These are all coterminal angles to radians.

Out of the given answers, is the only possible answer.

3

Find the coterminal angle of , if possible.

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 .

4

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

Explanation

To determine the coterminal angle, simply add or subtract increments or decrements of 360 degrees to the given angle.

For :

These angles can all be coterminal to 15 degrees. The only answer is .

5

Which of the following angles is coterminal to ?

Explanation

Which of the following angles is coterminal to ?

Coterminal angles are angles which start and end at the same point. In other words, they share both their starting and ending point. Note, this doesn't require them to be the same angle.

For instance, is coterminal with , because they both start on the positive x-axis, and end at the same place in quadrant 2.

So, we want to find an angle that ends at the same place in quadrant 1 as . Of the answer choices, only 1 ends in quadrant 1, so that one must be our answer:

6

Of the following choices, find a coterminal angle of .

Explanation

In order to find a coterminal angle, simply add or subtract radians to the given angle as many times as possible.

The possible angles after adding increments of radians are:

The possible angles after subtracting decrements of radians are:

Out of the given possibilities, only is a valid answer.

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