trig identities. what is an identity? identity: a statement of equality that is true as long as...

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TRIG IDENTITIES

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Page 1: TRIG IDENTITIES. What is an identity?  Identity: a statement of equality that is TRUE as long as neither side is undefined. Except when x = -1

TRIG IDENTITIES

Page 2: TRIG IDENTITIES. What is an identity?  Identity: a statement of equality that is TRUE as long as neither side is undefined. Except when x = -1

What is an identity?

Identity: a statement of equality that is TRUE as long as neither side is undefined.

Except when x = -1

Page 3: TRIG IDENTITIES. What is an identity?  Identity: a statement of equality that is TRUE as long as neither side is undefined. Except when x = -1

Basic Identities

Page 4: TRIG IDENTITIES. What is an identity?  Identity: a statement of equality that is TRUE as long as neither side is undefined. Except when x = -1

Why?

Page 5: TRIG IDENTITIES. What is an identity?  Identity: a statement of equality that is TRUE as long as neither side is undefined. Except when x = -1

Other identities based on P.T. identity:

Page 6: TRIG IDENTITIES. What is an identity?  Identity: a statement of equality that is TRUE as long as neither side is undefined. Except when x = -1

Cofunctions

A

B

Page 7: TRIG IDENTITIES. What is an identity?  Identity: a statement of equality that is TRUE as long as neither side is undefined. Except when x = -1

Cofunction Identities

Page 8: TRIG IDENTITIES. What is an identity?  Identity: a statement of equality that is TRUE as long as neither side is undefined. Except when x = -1

Sin(40) = Sin(-40)=

Cos(40)= Cos(-40)=

Page 9: TRIG IDENTITIES. What is an identity?  Identity: a statement of equality that is TRUE as long as neither side is undefined. Except when x = -1

Even-Odd Identities

Page 10: TRIG IDENTITIES. What is an identity?  Identity: a statement of equality that is TRUE as long as neither side is undefined. Except when x = -1

We will be doing 5 things with identities…

Evaluating – finding a value (numerical answer)

Simplifying – condensing (answer is usually a single trig function)

Factoring – un-doing the box/FOIL

Solving – getting “x” by itself (up to 4 possible solutions)

Verifying/Proving: showing that the left side and right side are equivalent.

Page 11: TRIG IDENTITIES. What is an identity?  Identity: a statement of equality that is TRUE as long as neither side is undefined. Except when x = -1

Ex 1. Evaluate

Find the value of sine & cosine if

Page 12: TRIG IDENTITIES. What is an identity?  Identity: a statement of equality that is TRUE as long as neither side is undefined. Except when x = -1

Ex 1. Find a trig function

Page 13: TRIG IDENTITIES. What is an identity?  Identity: a statement of equality that is TRUE as long as neither side is undefined. Except when x = -1

Ex 2. Simplify

Page 14: TRIG IDENTITIES. What is an identity?  Identity: a statement of equality that is TRUE as long as neither side is undefined. Except when x = -1

Ex 3. Factor

Page 15: TRIG IDENTITIES. What is an identity?  Identity: a statement of equality that is TRUE as long as neither side is undefined. Except when x = -1

Ex.4 Solve

Page 16: TRIG IDENTITIES. What is an identity?  Identity: a statement of equality that is TRUE as long as neither side is undefined. Except when x = -1

You Try

Page 17: TRIG IDENTITIES. What is an identity?  Identity: a statement of equality that is TRUE as long as neither side is undefined. Except when x = -1
Page 18: TRIG IDENTITIES. What is an identity?  Identity: a statement of equality that is TRUE as long as neither side is undefined. Except when x = -1
Page 19: TRIG IDENTITIES. What is an identity?  Identity: a statement of equality that is TRUE as long as neither side is undefined. Except when x = -1