Essential Question: How do I use trig identities to solve equations and verify identities?

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Essential Question How do I use trig identities
to solve equations and verify identities?

• How do I use the double angle and half angle
  formulas?

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Double Angle Formulas
sin 2?
2 sin ? cos ?
cos 2?
cos2? - sin2?
2cos2? - 1
1 2 sin2?
tan 2?
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generating the Double Angle Identities
sin(? ?)
sin(? ? )
sin(2?)
You will not have to regenerate these. This is
just for entertainments sake.
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generating the Double Angle Identities
cos(? ?)
cos(? ?)
cos(2?)
cos2? - (1 - cos2?)
cos2? - 1 cos2?
cos(2?)
You will not have to regenerate these. This is
just for entertainments sake.
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generating the Double Angle Identities
cos(? ?)
cos(? ? )
cos(2?)
(1 - sin2?) - sin2?
cos(2?)
You will not have to regenerate these. This is
just for entertainments sake.
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generating the Double Angle Identities
tan(? ?)
tan(? ? )
tan(2?)
You will not have to regenerate these. This is
just for entertainments sake.
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Ex. 1
Use the following to find sin2?, cos2? and tan2?
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-12
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Ex. 1
Use the following to find sin2?, cos2? and tan2?
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Ex. 1
Use the following to find sin2?, cos2? and tan2?
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Ex. 2
and ? terminates in the first
quadrant, find the exact value of sin2?, cos2?
and tan 2?.
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You Try!!
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What are your questions??
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Half-Angle Identities
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Half-Angle Identities

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Example Finding an Exact Value

• Find the exact value of sin (?/8).

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Example Finding an Exact Value

• Find the exact value of tan 22.5? using the
  identity
• Since 22.5? replace A with 45?.

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Example Finding an Exact Value continued

• Multiply the numerator and denominator by 2, than
  rationalize the denominator.

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Example Verifying identities

• Verify that 1 cos 2x sec2x tan2x is an
  identity.

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Example Simplifying Expressions

• Simplify

• Solution