Prove the Pythagorean identity sin[math]^2\theta +[/math] cos[math]^2\theta = 1[/math].
[list=1] [*]Draw a labeled diagram of a right triangle. [*]Apply the Pythagorean Theorem to this triangle. [*]Divide both sides of this equation by [math]r^2[/math]. [*]Rewrite this equation using the laws of exponents. [*]Find sin [math]\theta[/math] and cos [math]\theta[/math] by looking at the diagram. [*]Substitute sin [math]\theta[/math] and cos [math]\theta[/math] into the equation from step 4. [*]Rewrite the equation using the standard notation for trigonometric functions with exponents. [/list]