Find the solution in quadrant II for 5 + 10sin(5x) = 10. θ>0

Question

Find the solution in quadrant II for 5 + 10sin(5x) = 10. θ>0

x=

Answer 1

sin(5x) = 1/2; 5x = π/6 + 2πn; x = π/30 + 2πn/5 or 5x = 5π/6 + 2πn. x = π/6 + 2πn/5

1. Let take x = π/30 + 2πn/5; n = 2 x = π/30 + 24π/30 = 5π/6
2. Let x = π/6 + 2πn/5, n = 1 x = π/6 + 2π/5 = 17π/30, n = 2 x = π/6 + 4π/5 = 29π/30

Answer: 5π/6, 17π/30, 29π/30

Answer 2

5 + 10sin(5x) = 10

10sin(5x) = 5

sin(5x) = 1/2

sin(x) = 1/2 at π/3 + 2nπ or 2π/3 + 2nπ, n = 0, 1, 2, 3, 4, ...

5x = π/3 + 2nπ

5x = 2π/3 + 2nπ

x = π/15 + 2/5nπ = π/15, 7π/15, 13π/15, 19π/15, ..

x = 2π/15 + 2/5nπ = 2π/15, 8π/15, 14π/15, 20π/15, ..

In quadrant 2, π/2 < x < π

Solutions are 8π/15, 13π/15, 14π/15