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.

This circle has the centre at the origin and a radius of 1 unit. The point P can move around the circumference of the circle. At point P the \(x\)-coordinate is \(\cos{\theta}\) and the \(y ...