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In this interactive applet, the radian measure of an angle is defined.
Initially, a blue circle of certain radius length is shown. By dragging the "Angle" slider, a central angle is created along with the subtended arc. As the angle and its subtended arc increase, a stack of radii is built up to show how many radii the length of the arc is equal to. This number is the radian measure of the central angle and it is shown along with its degree measure. And since this number shows how many radii the length of the subtended arc is equal to, it can be expressed algebraically as the ratio of the length of the arc over the length of the radius of the circle. This ratio is also shown to the right part of the slider. By dragging the “Radius” slider to change the radius of the circle while keeping the same angle, that ratio remains unchanged. Thus, the length of the arc intercepted by an angle is proportional to the radius, and the constant of proportionality is defined as the radian measure of the angle.
A detailed description is also included in the product as a printable word document.
To be able to see and play with the applet you will need to download and install the free software GeoGebra in your computer or tablet if you haven’t done this before. The process is very simple and quick: The link is
from which you can download GeoGebra Classic 5 (this is the version that I also use).