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5.5 Multiple-Angle and Product-Sum Formulas

5.5 Multiple-Angle and Product-Sum Formulas. Find all solutions in. Sketch the graph of y = 4 cos 2 x - 2 over. = 2(2 cos 2 x - 1). = 2 cos 2x. Use the fact that. to find sin 2x, cos 2x, and tan 2x. sin 2x = 2 sin x cos x =. cos 2x = 2 cos 2 x - 1 =. 5. tan 2x =. -12. 13.

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5.5 Multiple-Angle and Product-Sum Formulas

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  1. 5.5 Multiple-Angle and Product-Sum Formulas

  2. Find all solutions in

  3. Sketch the graph of y = 4 cos2 x - 2 over = 2(2 cos2 x - 1) = 2 cos 2x

  4. Use the fact that to find sin 2x, cos 2x, and tan 2x sin 2x = 2 sin x cos x = cos 2x = 2 cos2 x - 1 = 5 tan 2x = -12 13

  5. Express sin 3x in terms of sin x. sin 3x = sin (2x + x) = sin 2x cos x + cos 2x sin x = 2 sin x cos x cos x + (1 - 2 sin2 x) sin x = 2 sin x cos2 x + sin x - 2 sin3 x = 2 sin x(1 - sin2 x) + sin x - 2 sin3 x = 2 sin x - 2 sin3 x + sin x - 2 sin3 x = 3 sin x - 4 sin3 x

  6. Rewrite sin4 x as a sum involving first powers of cos x sin4 x = (sin2x)2 Foil

  7. Find the exact value of sin 105o sin of 105 is positive sin 105o =

  8. Writing Products as Sums Rewrite cos 5x sin 4x as a sum or difference. cos 5x sin 4x =

  9. Using a Sum-to-Product Formula Find the exact value of cos 1950 + cos 1050 cos 1950 + cos 1050 = 2 cos 1500 cos 450

  10. Solving a Trigonometric Equation Find all solutions of sin 5x + sin 3x = 0 in 2sin 4x cos x = 0 sin 4x = 0 cos x = 0 Plug in 0, 1, 2, and 3

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