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Chapter 5.4 Multiple Angle Identities

Chapter 5.4 Multiple Angle Identities. Learning Target: I can apply the double-angle identities, power-reducing identities, and half angle identities. Double Angle Identities. Sin(2u) = 2sin(u)cos(u) Cos(2u) = Tan(2u) = 2tan(u) / (1 – tan 2 (u)). Cos 2 (u) – sin 2 (u) 2cos 2 (u) – 1

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Chapter 5.4 Multiple Angle Identities

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  1. Chapter 5.4Multiple Angle Identities Learning Target: I can apply the double-angle identities, power-reducing identities, and half angle identities.

  2. Double Angle Identities • Sin(2u) = 2sin(u)cos(u) • Cos(2u) = • Tan(2u) = 2tan(u) / (1 – tan2(u)) Cos2(u) – sin2(u) 2cos2(u) – 1 1 – 2sin2(u)

  3. Power Reducing Identities • Sin2(u) = (1 – cos(2u))/2 • Cos2(u) = (1 + cos(2u))/2 • Tan2(u) = (1 – cos(2u)) / (1 + cos(2u))

  4. Examplereducing a power • Rewrite cos4(x) with no power great than 1.

  5. Half-Angle Identities

  6. Homework Pg. 475 # 3 – 36 every 3rd

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