# SAT Mathematics : Using Radians

## Example Questions

### Example Question #1 : Circles

Explanation:

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

Now we can write:

### Example Question #1 : Circles

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?

Explanation:

Since , we can solve by setting up a proportion:

Cross multiply and solve.

### Example Question #2 : Circles

Change the following expression to degrees:

Explanation:

First, we need to simplify the expression:

Now multiply by :

### Example Question #1 : Circles

Convert the following expression to radians:

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:

Explanation:

First, we need to simplify the expression:

Then multiply by :

### Example Question #3 : Using Radians

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?

Explanation:

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

.

### Example Question #3 : Using Radians

Explanation:

We know that:

since the giving angle was in degrees then we multiply