Quick and Useful Trigonometry Cheat Sheet, Cheat Sheet of Trigonometry

Download Quick and Useful Trigonometry Cheat Sheet and more Cheat Sheet Trigonometry in PDF only on Docsity! Math 150 T17-Trig “Cheat Sheet” Page 1 MATH 150 – TOPIC 17 TRIG “CHEAT SHEET” Definition of the Six Trigonometric Functions Right triangle definitions, where 0 < θ < π/2. Opposite Adjacent Hypotenuse θ sin θ = opposite hypotenuse csc θ = hypotenuse opposite cos θ = adjacent hypotenuse sec θ = hypotenuse adjacent tan θ = opposite adjacent cot θ = adjacent opposite Unit circle definitions, where θ is any angle. y x 1 • • θ 1 1 (x, y) y x 1 = √ x2 + y2 sin θ = y 1 = y csc θ = 1 y cos θ = x 1 = 1 sec θ = 1 x tan θ = y x cot θ = x y Thus, x = cos θ, y = sin θ Reciprocal Identities sin x = 1 csc x sec x = 1 cos x tanx = 1 cot x csc x = 1 sin x cos x = 1 sec x cotx = 1 tanx Tangent and Cotangent Identities tan x = sin x cos x cotx = cos x sin x Pythagorean Identities sin2 x + cos2 x = 1, 1 + tan2 x = sec2 x, 1 + cot2 x = csc2 x Reduction Formulas sin(−x) = − sin x cos(−x) = cos x csc(−x) = − csc x tan(−x) = − tanx sec(−x) = sec x cot(−x) = − cotx Sum and Difference Formulas sin(u ± v) = sin u cos v ± cos u sin v cos(u ± v) = cos u cos v ∓ sin u sin v tan(u ± v) = tan u ± tan v 1 ∓ tanu tan v Cofunction Identities sin (π 2 − x ) = cos x cos (π 2 − x ) = sin x csc (π 2 − x ) = sec x tan (π 2 − x ) = cot x sec (π 2 − x ) = csc x cot (π 2 − x ) = tan x Double Angle Formulas sin 2u = 2 sin u cosu cos 2u = cos2 u − sin2 u = 2 cos2 u − 1 = 1 − 2 sin2 u tan 2u = 2 tanu 1 − tan2 u Half Angle Formulas sin2 u = 1 − cos 2u 2 cos2 u = 1 + cos 2u 2 tan2 u = 1 − cos 2u 1 + cos 2u Continued on next page