Find all of the exact solutions to the following equation. (Use the parameter k as necessary to represent any integer. Enter your answers as a comma-separated list.)

Question

sin(x/3)=(sqrt2)/(2)

Find all of the exact solutions to the following equation. (Use the parameter k as necessary to represent any integer. Enter your answers as a comma-separated list.)

Answer 1

sin(x/3) = √2/2

x / 3 = π/4 + 2kπ or 3π/4 + 2kπ

So, x = 3π/4 + 6kπ or 9π/4 + 6kπ, where k = 0, ±1, ±2, ...