1. Trigonometric Identities
Lesson 5-1

2. 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

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 )

4. 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.

5. 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)

6. 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