Graphs of Sine and Cosine
Cosine and sine of an angle are defined to be the and -coordinates of the point on the unit circle with the property that the line from to makes and angle with the positive -axis.
The applet below 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 the point moves once around the circle it returns to its original position - this is the reason and are periodic.