3θ = or 3θ = for k Z = or =, for k Z. θ θ 17. 2 cos (2θ) = cos(2θ) = 2θ = or 2θ = for k Z = or = , for k Z. θ θ 19. 2 cos (3θ) = cos(3θ) = 3θ = or 3θ = for k Z = or = , for k Z. θ θ 21. cos (θ) = = , for k Z θ = for k Z. θ 23. 2 sin (θ) = sin (θ) = = or = for k Z θ θ = or = , for k Z. θ θ 25. sin (x) = 0.27 = sin-1 (0.27) x = 0.2734 + 2kπ or = 0.2734 + 2kπ, for k Z. x x π Since 0 2π, there are two answers, = 0.2734 and = 0.2734 = 2.8682. x< x x ≤ π 27. sin (x) = = sin-1 () x = 0.6187 + 2kπ or (– 0.6187) + 2kπ, for k Z. x x = – π – Since 0 < 2π, there are two answers, = 0.6187 + 2π = 5.6645 and = (– 0.61873) = x x x ≤ – π – 3.7603. 29. cos (x) = = cos-1 ( x
3θ = or 3θ = for k Z θ = or θ =, for k Z. 17. 2 cos (2θ) = cos(2θ) = 2θ = or 2θ = for k Z θ = or θ = , for k Z. 19. 2 cos (3θ) = cos(3θ) = 3θ = or 3θ = for k Z θ = or θ = , for k Z. 21. cos (θ) = θ = , for k Z θ = for k Z. 23. 2 sin (θ) = sin (θ) = θ = or θ = for k Z θ = or θ = , for k Z. 25. sin (x) = 0.27 x = sin-1 (0.27) x = 0.2734 + 2kπ or x = π 0.2734 + 2kπ, for k Z. Since 0 ≤ x< 2π, there are two answers, x = 0.2734 and x = π 0.2734 = 2.8682. 27. sin (x) = x = sin-1 () x = – 0.6187 + 2kπ or x = π – (– 0.6187) + 2kπ, for k Z. Since 0 ≤ x < 2π, there are two answers, x = – 0.6187 + 2π = 5.6645 and x = π – (– 0.61873) = 3.7603. 29. cos (x) = x = cos-1 (
Chapter%206%20Solutions.docx