# High School Math : Understanding Radians and Conversions

## Example Questions

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### Example Question #31 : Trigonometry

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 #1 : 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 #13 : The Unit Circle And Radians

How many degrees are in  radians?

Explanation:

Cross multiply:

Notice that the 's cancel out:

### Example Question #32 : Trigonometry

How many radians are in ?

Explanation:

### Example Question #31 : Trigonometry

Explanation:

Since , we can convert as follows:

### Example Question #16 : The Unit Circle And Radians

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 #17 : The Unit Circle And Radians

How many radians are in ?

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?

Explanation:

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

Cross multiply:

Divide both sides by :

### Example Question #41 : Trigonometry

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 #20 : The Unit Circle And Radians

How many degrees are in  radians?