3.8 Fundamental Identities. Ex 1) Use definitions to prove: –A trig identitiy is a trig equation that is always true –We can prove an identity using the.

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Presentation transcript:

3.8 Fundamental Identities

Ex 1) Use definitions to prove: –A trig identitiy is a trig equation that is always true –We can prove an identity using the definitions of trig functions (they use x, y, and r)

We also have the Pythagorean Identities “I tan in a second” (get by ÷ by cos 2 θ) “I cotan in a cosecond” (get by ÷ by sin 2 θ)

We can prove identities (using θ, ϕ, β, etc) or verify the identity using specific values. Ex 2) Use exact values to verify the identity for the given θ a) 60° 1 LHS: RHS:

Ex 2) Use exact values to verify the identity for the given θ b) 150° 30° 1 LHS: RHS:

Other Identities to use: Ratio: Reciprocal: Pythagorean Identities: (already mentioned) Odd/ Even:

(try ratio & reciprocal) b) Ex 3) Simplify by writing in terms of sine & cosine a)  Pythag (1 + tan 2 θ = sec 2 θ)  odd/even 1

Homework #308 Pg 169 #1–45 odd Hints for HW  Make sure calculator is in correct MODE  Draw those reference triangle pictures!