High School Math : The Unit Circle and Radians

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #11 : The Unit Circle And Radians

What is the value of the angle  radians when converted to degrees?

Possible Answers:

Correct answer:

Explanation:

The answer can be found using the conversion of 1 radian equals  degrees.  Multiplying  by this conversion factor gives 270 degrees.

Example Question #12 : The Unit Circle And Radians

A point has Cartesian coordinates . Rewrite this as an ordered pair in the polar coordinate plane, rounding the coordinates to the nearest hundredth.

Possible Answers:

Correct answer:

Explanation:

Set . Calculate the polar coordinates  as follows:

Example Question #13 : The Unit Circle And Radians

How many degrees are in  radians?

Possible Answers:

Correct answer:

Explanation:

Cross multiply:

Notice that the 's cancel out:

Example Question #14 : The Unit Circle And Radians

How many radians are in ?

Possible Answers:

Correct answer:

Explanation:

The relationship between degrees and radians is  radians. Therefore,  would be  radians.

Example Question #15 : The Unit Circle And Radians

Express in radians: 

Possible Answers:

Correct answer:

Explanation:

Since , we can convert as follows:

Example Question #16 : The Unit Circle And Radians

How many radians are in ?

Possible Answers:

Correct answer:

Explanation:

Since there are  radians for every , we can set up a proportion to solve.

Cross multiply.

Divide both sides by .

Example Question #17 : The Unit Circle And Radians

How many radians are in ?

Possible Answers:

Correct answer:

Explanation:

The conversion for radians is , so we can make a ratio:

Cross multiply:

Isolate :

Example Question #18 : The Unit Circle And Radians

How many degrees are in  radians?

Possible Answers:

Correct answer:

Explanation:

The conversion for radians is , so we can make a ratio:

Cross multiply:

Divide both sides by :

Example Question #19 : The Unit Circle And Radians

How many degrees are in  radians?

Possible Answers:

Correct answer:

Explanation:

The conversion for radians is , so we can make a ratio:

Cross multiply:

Notice that the 's cancel out:

 

Example Question #20 : The Unit Circle And Radians

How many degrees are in  radians?

Possible Answers:

Correct answer:

Explanation:

The conversion for radians is , so we can make a ratio:

Cross multiply:

Notice that the 's cancel out:

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