RADIAN CREATOR
by Mr. Landry

I am assuming that you have gone over the tutorial on radians here. You must have Java installed in order to use the interactive module that I created below. If you do not see the java icon, , as this module loads then you do not have Java installed.

Get Java here

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WHAT IS A RADIAN?
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You are conditioned to use degrees to measure an angle. But there is an alternative system for measuring angle called "radians."

A "radian" is a measure of a central angle of a circle. If you wrap the radius of a circle on the circumference of a circle producing an arc, the central angle created with the endpoints of the arc connected to the center of the circle is called "1 radian." See image below.

For each radius placed on the circumference of a circle you increase the radian measure. See image below.

The radian measuring system is very useful in the world of mathematics and science and is used often in the area of mathematics called Trigonometry.

Below are some important questions to consider when working with the radian measuring system:

1) How many radians are there in a circle of 360°?

ANS: Remember radians are a measure of an ANGLE.

The Logic
s1) For every 1 radius on the outside of a circle an angle of 1 radian is produced, Right? Yes!

s2) I can find how many radii are on the outside of a circle with the circumference formula, C = 2π(radius). This formula lets me know there are 2π radii in any circle.
...If you don't understand what I just said it means you don't fully comprehend what multiplication means. For example, 3 x 4 tells you how many 4's are added, i.e. 4 + 4 + 4 , three 4's are added. So the first number tells you HOW MANY of the second numbers there are. So, 2π(radius) or 6.28 x radius tells me how many radii are in a circle - See image below.

So have two systems of measuring an angle - degrees or radians.
The angle measure around a circle is 360° or 2π radians or 6.28 radians

2) How many degrees in 1 radian?
ANS: You can use the concept of ratios to produce a proportion. Since for every 360° there are 2π radians. Hence,

or

Put in 1 in R for 1 radian and solve for D to determine the number of degrees.

There are approximately 57.296° in an angle of 1 radian.

3) If one circle has a larger radius than another circle will the larger circle have more radians than the smaller circle and vise-versa?
ANS: No, just like ALL circles have 360° all circles have the same number of radians. This is what the Geogebra applet below will show you!

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YOUR GOAL WITH THE INTERACTIVE MODULE BELOW
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...How do you construct an angle measure of 1 radian? 2 radians? 2.6 radians? etc.

...What is the degree measure of a central angle with a radian measure of 1 radian? 2 radians? 3 radians? etc.

...Approximately how many radians are there in a circle of radius 1? A circle of radius 2? a circle of radius 4? etc.