How to derive the sine of a sum formula.
How to derive the cosine of a difference formula.
How to use the sine and cosine addition formulas to prove the double-angle formulas.
How to derive the equation for a circle using the distance formula.
How to derive the equation for the distance between two points using the Pythagorean Theorem.
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.