Chapter 5.3 Sum and Difference Identities

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Chapter 5.3Sum and Difference Identities

• Learning Target I can apply the identities for
  the cosine, sine, and tangent of a difference or
  sum

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Cosine of a Sum or Difference

• cos (u v) cos(u)cos(v) sin(u)sin(v)
• cos (u v) cos(u)cos(v) sin(u)sin(v)

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Sine of a Sum or Difference

• sin (u v) sin(u)cos(v) cos(u)sin(v)
• Sin (u v) sin(u)cos(v) cos(u)sin(v)

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Tangent of a Sum or Difference

• Tan (u v) (tan(u) tan(v)) / (1
  tan(u)tan(v))
• Tan (u v) (tan(u) - tan(v)) / (1
  tan(u)tan(v))

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Example

• Find the exact value of cos(15) without using a
  calculator.

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Example

• Write each of the following as the sine or cosine
  of an angle.
• Sin(22)cos(13) cos(22)sine(13)
• Cos(?/3)cos(?/4) sin(?/3)sin(?/4)
• Sin(x)sin(2x) cos(x)cos(2x)

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Homework

• Pg. 468
• 1 21 odd