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 use the unit circle to derive the tangent identity and the Pythagorean identity.
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 identities that are useful in graphing the reciprocal trigonometric functions.