Proof. Assume a point in the unit circle centered at the origin forming an angle . Let be a point on the x-axis corresponding to the x-coordinate of . Let be the origin. A right triangle would be formed: . The length of would be equal to and the length of would be equal to . The length of is 1 (since we're using the unit circle). Using the Pythagorean theorem, we have:
Due to this fundamental relationship, other Pythagorean Identities emerge through the use of:
the complimentary and cofunction properties
the reciprocal functions
the quotient identities
The other identities include:
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