SAT Mathematics : Circles

Study concepts, example questions & explanations for SAT Mathematics

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Example Questions

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Example Question #1 : Circles

Give  in radians:

Possible Answers:

Correct answer:

Explanation:

First we need to convert degrees to radians by multiplying by :

 

Now we can write: 

Example Question #1 : Circles

Give  in radians:

Possible Answers:

Correct answer:

Explanation:

First, we need to convert  to radians by multiplying by 

 

Now we can solve the following equation for :

Example Question #2 : Circles

How many degrees are in  radians?

Possible Answers:

Correct answer:

Explanation:

Since , we can solve by setting up a proportion:

Cross multiply and solve.

Example Question #2 : Circles

Change the following expression to degrees:

Possible Answers:

Correct answer:

Explanation:

First, we need to simplify the expression:

 

Now multiply by :

Example Question #1 : Circles

Convert the following expression to radians:

Possible Answers:

Correct answer:

Explanation:

First, we need to simplify the expression:

 

In order to change degrees to radians, we need to multiply by :

Example Question #6 : Circles

Simplify and give the following expression in degrees: 

Possible Answers:

Correct answer:

Explanation:

First, we need to simplify the expression:

Then multiply by :

Example Question #3 : Using Radians

Convert  radians into degrees.

Possible Answers:

Correct answer:

Explanation:

Recall the definition of "radians" derived from the unit circle:

The quantity of radians given in the problem is . All that is required to convert this measure into degrees is to denote the unknown angle measure in degrees by  and set up a proportion equation using the aforementioned definition relating radians to degrees:

Cross-multiply the denominators in these fractions to obtain:

or

.

Canceling like terms in these equations yields

Hence, the correct angle measure of  in degrees is .

Example Question #8 : Using Radians

 radians is equivalent to how many degrees?

Possible Answers:

Correct answer:

Explanation:

1 radian is equal to  degrees. Using this conversion factor,

.

Example Question #3 : Using Radians

Simplify your answer.

Convert  to radians:

Possible Answers:

Correct answer:

Explanation:

We know that:

 Radians

since the giving angle was in degrees then we multiply

Example Question #2 : Circles

Give your answer in terms of .

Convert   to radians:

Possible Answers:

Correct answer:

Explanation:

To convert degrees to radians, we need to multiply the given degree by .

To simplify, we get:

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