Two smallest positive solutions

Question

Solve 8sin(5x)=4 for the two smallest positive solutions A and B, with A < B. Answers should be accurate to two decimal places

Answer 1

sin(5x) = 1/2

So, 5x = π/6 + 2kπ or 5π/6 + 2kπ, k = 0, 1, -1, 2, -2, ...

x = π/30 + 2kπ/5 or π/6 + 2kπ/5

If k = 0, we have x = π/30 or π/6 ≈ 0.10 or 0.52

Answer 2

Solve 8sin(5x)=4 for the two smallest positive solutions A and B, with A < B. Answers should be accurate to two decimal places

Divide by 8 ( both sides)

Sin(5x) = 1/2

5x= Sin-1 (0.5) 5x = pi/6

(A)

x = pi/30

and

(B)

x = 2pi+pi/30 = 61pi/30