Trig. Identities

TRIG. IDENTITIES & FORMULAS Sum and Difference Formulas

Product to Sum 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 tan A tan B tan( A B )  1 tan A tan B tan A tan B tan( A B )  1 tan A tan B

1 sin A cos B   sin( A B ) sin( A B ) 2 1 cos A sin B   sin( A B ) sin( A B ) 2 1 cos A cos B   cos( A B ) cos( A B ) 2 1 sin A sin B   cos( A B ) cos( A B ) 2

Double-Angle Formulas

Sum to Product Formulas

sin 2 A 2 sin A cos A cos 2 A cos2 A sin 2 A cos 2 A 2 cos2 A 1 cos 2 A 1 2 sin 2 A 2 tan A tan 2 A  1 tan 2 A

st

1 Form 2nd Form 3rd Form

sin sin 2 sin

sin sin 2 cos

 2

cos



 2



sin 2 2   cos cos 2 cos cos 2 2   cos cos  2 sin sin 2 2

Half-Angle Formulas

A 1 cos A  2 2 A 1 cos A cos  2 2 A 1 cos A tan  2 sin A A sin A tan  2 1 cos A

Negative Angle Formulas

sin

sin( A) sin A cos( A) cos A tan(A) tan A 1st Form 2nd Form DERIVATIVES

sin2 x + cos2 x = 1 tan2 x + 1 = sec2 x 1 + cot2 x = csc2 x cos2 x = (1 + cos 2x) / 2 sin2 x = (1 – cos 2x) / 2

(d/dx) sin x = cos x (d/dx) cos x = - sin x (d/dx) tan x = sec2 x (d/dx) cot x = - csc2 x (d/dx) sec x = sec x tan x (d/dx) csc x = - csc x cot x