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Unit Circle: Sine and Cosine Functions

This sketch shows how we can create a function for sine and cosine. As a point goes around the unit circle, we can see how the different ratios change based on the angle, given here as and measured in radians. First, select Sine and then Animate. At each of the points on the traced out curve, the x-coordinate represents the angle and the y-coordinate represents the sine of the angle. Notice that the y-coordinates of and the point we are tracing are always the same. In this way, we can see how to graph the function: Cosine can be similarly graphed, but here we are plotting the -coordinate of for each angle .