Trigonometric Identities Lesson 5-1

An identity is a statement which is true for all values of the variable. x2 - 9 = (x+3)(x – 3) is an identity x2 – 9 = 0 is a conditional equation, it is only true when x = ±3

Some Fundamental Identities reciprocal identities (p. 312) quotient identities (p. 312) Pythagorean Identities sin2 θ + cos2 θ = 1 tan2 θ + 1 = sec2 θ cot2 θ + 1 = csc2 θ Cofunction Identities sin θ = cos (π/2 – θ) cos θ = sin (π/2 – θ) Odd-Even Identities cos(-θ ) = cos(θ ) sin (-θ ) = - sin(θ )

If sec x = 5/3, find cos x. If sin x = 3/5, and tan < 0, find cos x. If cot x = -3 and cos x > 0, find csc x. If sin x = 1/6 and cos x > 0, find cot x.

Matching 1. sec x cos x a) -1 2. cot x sin x b) 1 3. tan2x - sec2x c) cos x 4. (1-cos2x)(csc x) d) -tan x 5. sin (-x) e) cot x cos (-x) 6. sin (π/2 – x) f) sin x cos (π/2 – x)

Simplify csc x sec x – cot x Simplify sin x cos2x – sin x Add sin 𝑥 1+cosx + cos 𝑥 sin 𝑥 Rewrite without fractions 1 1+ cos 𝑥