# The unit circle and sin, cos and tan functions

- Author:
- wendy.burton3

- Topic:
- Circle, Functions, Unit Circle

## The unit circle and sin, cos and tan functions

On the left is a right angle triangle inside a unit circle.
The unit circle has a radius of one unit. Because the length of the hypotenuse
is always 1unit, the amplitude of the sine of angle a = the length of the
opposite side and the amplitude of the cosine of angle a = the length of the
adjacent side. The tangent is always sine / cosine.
Play with the position of point B on the circumference of
the circle.
Notice how the length of the opposite and adjacent sides
change as the angle changes. Notice also how the sine and cosine values change
accordingly.
On the right the sine, cosine and tangent
functions can be traced with the points E,F and G respectfully as the angle a
changes due to the repositioning of point B around the circle. To see the full
wavelength of each function check / uncheck the appropriate buttons.