9.4 Trigonometric identities

Ideas in this lesson

Pythagorean identities

Use sine squared plus cosine squared equals one and its divided forms, on the original domain.

Quotient and reciprocal identities

Replace tangent, cotangent, secant and cosecant with ratios involving sine and cosine. Retain all original restrictions.

Sum and difference formulas

Keep the signs in the angle addition formulas and use exact special-angle values.

Double-angle identities

A double-angle formula connects a function at twice an angle to functions at the original angle.

Half-angle identities and signs

Use the half-angle formula and choose the sign from the half-angle quadrant.

Derive a double-angle identity

Substitute equal angles into an addition formula, then combine like products.