Find all solutions in the interval [0, 2π). (sin x)(cos x) = 0

Solution:

Unlike normal solutions of algebraic equations with the number of solutions based on the degree of the variable, in trigonometric equations, the solutions are of two types, based on the different value of angle for the

trigonometric function, for the same solution.

Given (sin x)(cos x) = 0

If (sin x)(cos x) = 0 then either (sin x) = 0 or (cos x) = 0

For sin x = 0; x = 0, π , 2π.

For cosx = 0; x = π/2, 3π/2

Therefore, the solutions are 0,π, 2π π/2, 3π/2.

Find all solutions in the interval [0, 2π). (sin x)(cos x) = 0

Summary:

All solutions in the interval [0, 2π) when (sin x)(cos x) = 0 are 0,π, 2π π/2, 3π/2.