1. 2 sin (θ) = sin (θ) = = + or = for k Z. θ θ π Since 0 < 2π, the answers should be = and =. ≤ θ θ θ 3. 2 cos(θ) = 1 cos(θ) = = or = 2π for k Z. θ θ Since 0 < 2π, the answers should be = and = . ≤ θ θ θ 5. sin (θ) = 1 = + 2kπ, for k Z. θ Since 0 < 2π, the answer should be = . ≤ θ θ 7.cos(θ) = 0 = or = 2π for k Z. θ θ Since 0 < 2π, the answers should be = and = . ≤ θ θ θ 9. 2 cos (θ) = cos(θ) = = or = 2π for k Z. θ θ 11. 2 sin (θ) = sin (θ) = = or = for k Z. θ θ 13. 2 sin (3θ) = sin (3θ) = 3θ = or 3θ = for k Z = or = , for k Z. θ θ 15. 2 sin (3θ) = sin (3θ) =
1. 2 sin (θ) = sin (θ) = θ = + or θ = π for k Z. Since 0 ≤ θ < 2π, the answers should be θ = and θ =. 3. 2 cos(θ) = 1 cos(θ) = θ = or θ = 2π for k Z. Since 0 ≤ θ < 2π, the answers should be θ = and θ = . 5. sin (θ) = 1 θ = + 2kπ, for k Z. Since 0 ≤ θ < 2π, the answer should be θ = . 7.cos(θ) = 0 θ = or θ = 2π for k Z. Since 0 ≤ θ < 2π, the answers should be θ = and θ = . 9. 2 cos (θ) = cos(θ) = θ = or θ = 2π for k Z. 11. 2 sin (θ) = sin (θ) = θ = or θ = for k Z. 13. 2 sin (3θ) = sin (3θ) = 3θ = or 3θ = for k Z θ = or θ = , for k Z. 15. 2 sin (3θ) = sin (3θ) =
Chapter%206%20Solutions.docx