Formation of a Sinusoid from the Unit Circle
- Author:
- jeromeawhite
- Topic:
- Circle, Cosine, Sine, Trigonometry, Unit Circle
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.