## A “Proof by Picture” of the Angle Addition Formulas

All you need to know in order to follow the proof is:

- The basic trig identities:
- The center angle of the triangle is
.**Θ** - The hypotenuse is
(a radius of the unit circle).**1** - The side adjacent is
.*cos Θ* - The side opposite is
.*sin Θ* - The angle between the adjacent and opposite sides is a right angle.

- The center angle of the triangle is
- That any triangle can be scaled by a factor
:**H**- The angles stay the same.
- The sides are all multiplied by
.**H** - The hypotenuse in this example would become
.**1 × H = H**