Tutorial Services – Mission del Paso Campus

Trigonometric Identities & Formulas Tutorial Services Mission del Paso Campus Reciprocal Identities Ratio or Quotient Identities 1 1 sin x cos x sin x csc x tan x cot x . csc x sin x cos x sin x 1 1. cos x sec x sinx = cosx tanx cosx = sinx cotx sec x cos x 1 1. tan x cot x . cot x tan x Pythagorean Identities Pythagorean Identities in Radical Form sin x cos x 1. 2 2. sin x 1 cos2 x 1 tan 2 x sec2 x 1 cot 2 x csc2 x tan x sec 2 x 1. Note: there are only three, basic Pythagorean identities, the other forms cos x 1 sin 2 x are the same three identities, just arranged in a different order. Confunction Identities Odd-Even Identities Also called negative angle identities . sin x cos x cos x sin x Sin (-x) = -sin x Csc (-x) = -csc x 2 2 . Cos (-x) = cos x Sec (-x) = sec x . tan x cot x cot x tan x Tan (-x) = -tan x Cot (-x) = -cot x 2 2 . c sec x csc x csc x sec x Phase Shift =. 2 2 b 2 . Period =. b Sum and Difference Formulas/Identities How to Find Reference Angles sin(u v ) sin u cos v cos u sin v Step 1: Determine which quadrant the angle is in sin(u v ) sin u cos v cos u sin v Step 2: Use the appropriate formula Quad I = is the angle itself cos(u v ) cos u cos v sin u sin v Quad II = 180 or.

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