Imagine you're watching a dot travel around a circle of radius 1. This special circle, with radius exactly 1 and center at the origin, is called the unit circle.

When the dot moves around the circle, the angle it creates (from the positive x-axis) determines two important values:

• Cosine (cos): the horizontal position (x-coordinate) of the dot on the circle.

• Sine (sin): the vertical position (y-coordinate) of the dot on the circle.

In other words:

So cosθ and sinθ are, respectively, the base and height of a right angled triangle with hypotenuse of length 1, forming an angle of θ with the x-axis.

If we trace the values of sinθ and cosθ with θ on the x-axis, we find their sinusoidal graphs: