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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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slide2

–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
We also have the Pythagorean Identities

“I tan in a second”

(get by ÷ by cos2θ)

“I cotan in a cosecond”

(get by ÷ by sin2θ)

slide4

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:

other identities to use

Reciprocal:

Other Identities to use:

Ratio:

Pythagorean Identities: (already mentioned)

Odd/ Even:

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Ex 3) Simplify by writing in terms of sine & cosine

a)

(try ratio & reciprocal)

b)

 Pythag (1 + tan2θ = sec2θ)

 odd/even

1

homework
Homework

#308 Pg 169 #1–45 odd

Hints for HW  Make sure calculator is in correct MODE

 Draw those reference triangle pictures!