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3.8 Fundamental Identities. –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). Ex 1) Use definitions to prove:. We also have the Pythagorean Identities. “I tan in a second”.
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–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) Ex 1) Use definitions to prove:
We also have the Pythagorean Identities “I tan in a second” (get by ÷ by cos2θ) “I cotan in a cosecond” (get by ÷ by sin2θ)
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) LHS: 60° 1 RHS:
Ex 2) Use exact values to verify the identity for the given θ b) 1 150° 30° LHS: RHS:
Reciprocal: Other Identities to use: Ratio: Pythagorean Identities: (already mentioned) Odd/ Even:
Ex 3) Simplify by writing in terms of sine & cosine a) (try ratio & reciprocal) b) Pythag (1 + tan2θ = sec2θ) 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!