High School Math : The Unit Circle and Radians

Study concepts, example questions & explanations for High School Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #31 : The Unit Circle And Radians

How many degrees are in  radians?

Possible Answers:

Correct answer:

Explanation:

The ratio between radians and degrees is  radians.

That means we can set up a proportion:

Notice that the 's cancel out.

Example Question #32 : The Unit Circle And Radians

How many degrees are in  radians?

Possible Answers:

Correct answer:

Explanation:

The conversion rate for degrees and radians is  .

Set up a proportion to solve.

Cross multiply.

Notice that the  cancels out.

Example Question #33 : The Unit Circle And Radians

How many degrees are in radians?

Possible Answers:

Correct answer:

Explanation:

The ratio of degrees to radians is . Set up a proportion and solve.

Notice that the 's cancel out.

Example Question #34 : The Unit Circle And Radians

How many radians are in ?

Possible Answers:

Correct answer:

Explanation:

The relationship between degrees and radians is . We can set this up as a proportion to solve:

Example Question #35 : The Unit Circle And Radians

Convert  to radians. 

Possible Answers:

Correct answer:

Explanation:

Multiply the given degrees measurement by .

Simplify and you get

Example Question #36 : The Unit Circle And Radians

Convert  to degrees. 

Possible Answers:

Correct answer:

Explanation:

Multiply by  and then simplify. The answer is 

Example Question #37 : The Unit Circle And Radians

How many radians are in ?

Possible Answers:

Correct answer:

Explanation:

The ratio of degrees to radians is . Set up a proportion and solve.

Example Question #38 : The Unit Circle And Radians

How many degrees are in  radians?

Possible Answers:

Correct answer:

Explanation:

The conversion between radians and degrees is . We can use this as a ratio to solve:

Cross multipy.

Notice that the 's cancel out.

Example Question #39 : The Unit Circle And Radians

How many degrees are in radians?

Possible Answers:

Correct answer:

Explanation:

The conversion between radians and degrees is . We can then create a ratio to solve:

Cross multipy:

Notice that the 's cancel out.

Example Question #40 : The Unit Circle And Radians

If Angle  equals , what is the equivalent angle in radians (to the nearest hundredth)? 

Possible Answers:

Correct answer:

Explanation:

To convert between radians and degrees, it is important to remember that: 

With this relationship in mind, we can convert from degrees to radians with the following formula:


 

Learning Tools by Varsity Tutors