Basic Trigonometric Identities

Pythagorean Identities

cos² q + sin² q = 1

1 + tan² q = sec² q

1 + cot² q = csc² q

Fundamental Identities (as a result of symmetry of trig functions)

sin q = − sin(−q) csc q = − csc(−q)

cos q = cos(−q) sec q = sec(−q)

tan q = − tan(−q) cot q = − cot(−q)

Addition formulas

sin(a + b) = sin a cos b + cos a sin b

sin(a − b) = sin a cos b − cos a sin b

cos(a + b) = cos a cos b − sin a sin b

cos(a − b) = cos a cos b + sin a sin b

Double-angle formulas

sin 2a = 2 sin a cos a

cos 2a = cos² a − sin² a = 2 cos² a − 1 = 1 − 2sin² a

Trigonometric Derivatives