Sum of Squares of Sine and Cosine/Proof 3

Theorem

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

where $\sin$ and $\cos$ are sine and cosine.

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

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

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:


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