Goal:

## Theory:

Part 1

One radian is the angle of an arc created by wrapping the radius of a circle around its circumference.

In this diagram, the radius has been wrapped around the circumference to create an angle of 1 radian. The pink lines show the radius being moved from the inside of the circle to the outside:

The radius ‘r’ fits around the circumference of a circle exactly 2π times. That is why the circumference of a circle is given by:

circumference = 2πr

So there are 2π radians in a complete circle and π radians in a half-circle.

To convert radians to degrees, we make use of the fact that π radians equals one-half circle, or 180º.

This means that if we divide radians by π, the answer is the number of half circles. Multiplying this by 180º will tell us the answer in degrees.

So, to convert radians to degrees, multiply by 180/π, like this:

To convert degrees to radians, first find the number of half circles in the answer by dividing by 180º. But each half-circle equals π radians, so multiply the number of half circles by π.

So, to convert degrees to radians, multiply by π/180, like this:

## Method:

Part 2

Maths Helper Plus can show you the working steps for converting your angles between radians and degrees. It also draws the angle as an arc of a circle.

We have created a Maths Helper Plus document to complement this topic. You can use it to practice the steps described below, and as a starting point for solving your own problems.

File name: ”Angle Converter.mhp’ File size: 7kb

If you choose ‘Open this file from its current location’, then Maths Helper Plus should open the document immediately. If not, try the other option: ‘Save this file to disk’, then run Maths Helper Plus and choose the ‘Open’ command from the ‘File’ menu. Locate the saved file and open it. If you do not yet have Maths Helper Plus installed on your computer, click here for instructions.

##### Step 2 Enter the angle to convert

Press the F5 key to display the parameters box:

The number in the ‘X’ edit box changes the type of conversion performed.

If ‘X’ is 1, then the ‘A’ value is converted from degrees to radians.

If ‘X’ is 2, then the ‘A’ value is converted from radians to degrees.

If necessary, click on the ‘X‘ edit box and set the value to 1 or 2, depending on the type of conversion you want to perform.

Click on the ‘A‘ edit box and enter the angle to convert. For degrees, just type a number. For radians, you can type a number, or you can enter a value in terms of π by using ‘pi‘ for π.

Click the ‘Update‘ button to update the calculations.

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