Patterns even emerge from the equations for these things...........

Unit Circle

The "Unit Circle" is a circle with a radius of 1.

Being so simple, it is a great way to learn and talk about lengths and angles.
The center is put on a graph where the x axis and y axis cross, so we get this neat arrangement here.

Sine, Cosine and Tangent

Because the radius is 1, we can directly measure sine, cosine and tangent.

What happens when the angle, θ, is 0°?

cos 0° = 1, sin 0° = 0 and tan 0° = 0

What happens when θ is 90°?

cos 90° = 0, sin 90° = 1 and tan 90° is undefined

Try It Yourself!

Have a try! Move the mouse around to see how different angles (in radians or degrees) affect sine, cosine and tangent

The "sides" can be positive or negative according to the rules of Cartesian coordinates. This makes the sine, cosine and tangent change between positive and negative values also.