# High School Math : Understanding Radians and Conversions

## Example Questions

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### Example Question #1 : Understanding Radians And Conversions

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

Explanation:

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

### Example Question #2 : Understanding Radians And Conversions

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

Explanation:

Set . Calculate the polar coordinates  as follows:

### Example Question #3 : Understanding Radians And Conversions

How many degrees are in  radians?

Explanation:

Cross multiply:

Notice that the 's cancel out:

### Example Question #4 : Understanding Radians And Conversions

How many radians are in ?

Explanation:

### Example Question #5 : Understanding Radians And Conversions

Explanation:

Since , we can convert as follows:

### Example Question #6 : Understanding Radians And Conversions

How many radians are in ?

Explanation:

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

Cross multiply.

Divide both sides by .

### Example Question #7 : Understanding Radians And Conversions

How many radians are in ?

Explanation:

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

Cross multiply:

Isolate :

### Example Question #8 : Understanding Radians And Conversions

How many degrees are in  radians?

Explanation:

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

Cross multiply:

Divide both sides by :

### Example Question #9 : Understanding Radians And Conversions

How many degrees are in  radians?

Explanation:

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

Cross multiply:

Notice that the 's cancel out:

### Example Question #10 : Understanding Radians And Conversions

How many degrees are in  radians?