Sum of Squares of Sine and Cosine/Proof 3

Proof
Let $P = \tuple {x, y}$ be a point on the circumference of a unit circle whose center is at the origin of a cartesian plane.

From Sine of Angle in Cartesian Plane and Cosine of Angle in Cartesian Plane:
 * $P = \tuple {\cos \theta, \sin \theta}$

The graph of the unit circle is the locus of:
 * $x^2 + y^2 = 1$

as given by Equation of Circle.

Substituting $x = \cos \theta$ and $y = \sin \theta$ yields:


 * $\cos^2 \theta + \sin^2 \theta = 1$