Supplementary Function Identities

A trig identity based on $\pi$ transpositions

Prerequisites

In order for this identity to be valid, you must be able to discern a transposition of an angle that is of a whole # multiple of $\pi$

Examples

$\pi$ + $\theta$ $2\pi +\theta$ $-1\pi +\theta$ $5\pi -\theta$ $\theta -2\pi$

Theta is any angle at all

Process

Example with a transposition of $(3\pi +\theta )$

1. Pick an acute angle for angle $\theta$
2. List all trig functions Then make sure each function is equal to its normal version.
3. Now, lets add the acute angle we picked to our transposition. that is 3pi + pi/6. Find out what quadrant that is in. That is in quadrant 3. So, this means that only tangent is positive.
4. Update the trig functions list to match the positive changes. all others are negative.