How to derive the cosine of a difference formula.
How to derive the sine of a sum formula.
How to derive the formula for the midpoint of a segment in three dimensions.
How to derive the distance formula for polar coordinates.
How to use the distance formula to derive the equation for a circle.
How to derive two more cosine double-angle formulas.
How to use the power reduction formulas to derive the half-angle formulas.
How to use the unit circle to derive the tangent identity and the Pythagorean identity.
How to use the unit circle to derive identities that are useful in graphing the reciprocal trigonometric functions.