Verified answer

What "0 < x ≤ π" means is that you have to find a value for x

that is greater than 0 and less than or equal to π

if sin(3x) = 1, then 3x must be π/2 ( or 90 degrees) and 2k π

So, x = π/6 +2k π/3

k is any integer, so we want all the values of x <= π

if k = 0 then x = π//6

if k = 1 then x = π/6 + 2π/3 = π//6 + 4π/6 = 5 π/6 (which is less than π)

All other values of k make x greater than π or less than 0

so, the solutions are π/6 and 5π/6

if sin3x = 1, we need to change the limits also, so 0 < 3x <= 3π

3x = π/2,5π/2

x = π/6, 5π/6

sin(3x) = 1

sin(3x) = sin(pi/2 + 2pi * k)

3x = pi/2 + 2pi * k

3x = (pi/2) * (1 + 4k)

x = (pi/6) * (1 + 4k)

x = pi/6 , 5pi/6

k is an integer