Precalculus : Find the Measure of a Coterminal Angle

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #3 : Angles In The Coordinate Plane

Find the coterminal angle of 15 degrees.

Possible Answers:

Correct answer:

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.

Example Question #1 : Find The Measure Of A Coterminal Angle

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

Possible Answers:

Correct answer:

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.

Example Question #81 : Trigonometric Functions

Of the following choices, find a coterminal angle of .

Possible Answers:

Correct answer:

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.

Example Question #82 : Trigonometric Functions

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

 

Possible Answers:

Correct answer:

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 .

Example Question #83 : Trigonometric Functions

Find the coterminal angle of , if possible.

Possible Answers:

Correct answer:

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 .

Example Question #1 : Find The Measure Of A Coterminal Angle

Which of the following angles is coterminal to ?

Possible Answers:

Correct answer:

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: 

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