Prove that the coordinates of a particular angle on the unit circle are the cosine and sine of that angle.

Prove that the coordinates of a particular angle on the unit circle are the cosine and sine of that angle.

Consider the unit circle with coordinates x and y:


Cosine is defined as the side adjacent to the angle divided by the hypotenuse, (A/H), or in this case (x/1) so we see that cosine = x

Similarly sine is defined as the side opposite the angle divided by the hypotenuse, (O/H), or in this case (y/1) so we see that sine = 1

Thus we have proved that the coordinates of a particular angle on the unit circle are the cosine and sine of that angle, as shown below: