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Simple Trig Identities. Definition of An Identity. Any equation that is true for every number in the domain of the equation. Example 2x + 12 = 2(x + 6) Trig identities Pythagorean Identities Reciprocal identities Ratio identities. Pythagorean Identities. 90º. (x,y). r. y. θ. 0º.

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Presentation Transcript
definition of an identity
Definition of An Identity
  • Any equation that is true for every number in the domain of the equation.
  • Example
    • 2x + 12 = 2(x + 6)
  • Trig identities
    • Pythagorean Identities
    • Reciprocal identities
    • Ratio identities
pythagorean identities
Pythagorean Identities

90º

(x,y)

r

y

θ

  • Consider that
  • then

180º

x

360º

270º

ratio identities
Ratio Identities
  • Since we know that and
working with identities
Working with Identities
  • Start with one side and turn it into the other
  • If you get stuck work on the other side and see if you can make them the same
example
Example
  • Prove
working with identities1
Working with Identities
  • Tips
    • In an expression, look for a part of the expression that looks like part of one of the identities
    • Substitute that in
    • Look for factors to cancel
    • Look for terms of an expression that can be combined to form one of the identities
    • Also possible to look at identities in different forms
example1
Example
  • Prove
example2
Example
  • Prove
your turn
Your turn
  • Prove