Graphs of Cosine and Sine

Cosine and sine of an angle θ are defined to be the x and y-coordinates of the point P on the unit circle with the property that the line from O to P makes and angle θ with the positve x-axis.

cos(θ) is the x-coordinate of the point P and,
sin(θ) is the y-coordinate of the point P.

This applet shows how the graphs of sin(θ) and cos(θ) follow directly from the definition of these functions. Move the slider to change the angle. Observe that after the point moves once around the circle it returns to its original position - this is the reason cos and sin are periodic.

Jamie Mulholland
Department of Mathematics
Simon Fraser University
Created with GeoGebra