Sine and Cosine in the Unit Circle
- Author:
- ourcomedian
- Topic:
- Circle, Cosine, Functions, Sine, Trigonometry, Unit Circle
Note: This is a slight modification of Tutorial 8 of the Geogebra Intermediate Tutorial Series that can be found here: http://mathandmultimedia.com/2010/02/10/geogebratutorial8/
Instructions:
Move the slider in the bottom left to manipulate the size of angle θ from 0 to 2π (or press the play button in the bottom left and watch it oscillate).
Note that the dotted blue line segments are equal.
In order to trace point P, right-click the point in the left-hand column and check "trace on"
If we look at the properties of P, we can see that P is just defined as the point (d, y(C) (where d is the angle in radians). This is what a sine curve is--the y value of a point on the unit circle.
In order to do the same with cosine, deselect all the blue objects in the left hand column and select all the red objects. (Cumbersome, I know. Working on improving this!)