Verified answer

(sin(x) + 1)(sin(x) - 4) = 0 ..... 0 ≤ x ≤ 2pi

sin(x) = -1 ......... will be 0 if either factor is 0

⇒ x = π/2(4k - 1) or x = π/2(4k + 3) {k ∈ ℤ }

sin(x) = 4 ......... will be 0 if either factor is 0

⇒ has only complex solutions

in the interval 0 ≤ x ≤ 2pi, the only solution is:

x = 3π/2

Answer: x = 3π/2