Precalculus : Angles in the Coordinate Plane

Study concepts, example questions & explanations for Precalculus

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Example Questions

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Example Question #1 : Find The Degree Measure Of An Angle

Convert  radians to degrees.

Possible Answers:

Correct answer:

Explanation:

Write the conversion factor between radians and degrees.

Cancel the radians unit by using dimensional analysis.

Example Question #1 : Find The Degree Measure Of An Angle

Convert  to degrees.

Possible Answers:

Correct answer:

Explanation:

Write the conversion factor of radians and degrees.

Substitute the degree measure into .

Example Question #1 : Find The Degree Measure Of An Angle

Determine the angle  in degres made in the plane by connecting a line segment from the origin to .

 Assume 

Possible Answers:

Correct answer:

Explanation:

Firstly, since the point  is in the 3rd quadrant, it'll be between  and . If we take  to be the horizontal, we can form a triangle with base and leg of values  and . Solving for the angle in the 3rd quadrant given by

Since this angle is made by assuming  to be the horizontal, the total angle measure  is going to be:

 

Example Question #1 : Angles In The Coordinate Plane

Find the degree measure of  radians.  Round to the nearest integer.

Possible Answers:

Correct answer:

Explanation:

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

The nearest degree is .

Example Question #3 : Find The Degree Measure Of An Angle

Given a triangle, the first angle is three times the value of the second angle.  The third angle is .  What is the value of the second largest angle in degrees?

Possible Answers:

Correct answer:

Explanation:

A triangle has three angles that will add up to  degrees.

Convert the radians angle to degrees by substituting  for every .

The third angle is 60 degrees.

Let the second angle be .  The first angle three times the value of the second angle is .  Set up an equation that sums the three angles to .

Solve for .

Substitute  for the first angle and second angle.

The second angle is:  

The first angle is:  

The three angles are:  

The second highest angle is:  

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

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 #1 : Find The Measure Of A Coterminal Angle

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 #71 : 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 #1 : Find The Measure Of A Coterminal Angle

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 .

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