# Formation of a Sinusoid from the Unit Circle

- Author:
- flipkick70, jeromeawhite

- Topic:
- Circle, Cosine, Sine, Trigonometry

Based on your knowledge of the unit circle, see how sinusoids (sine and cosine waves) get their shapes.

Click the

**Start/Stop**button. Notice how both the green arc along the unit circle and the green line segment along the x-axis always maintain the same lengths. Therefore, the x-coordinate of point P also represents the radian measure of the arc's central angle. This can also be viewed as "unwrapping" the arc and laying along the x-axis, starting from the origin. Click the checkbox for either**sine**or**cosine**and once again observe how the geometry displayed on the unit circle is also represented sliding along the x-axis. Click the**trace**checkbox to view the formation of a sinusoid.