Find all the angles between 0 and 2pi satisfying the condition sinx=√(2) /2

Question

Find all the angles between 0 and 2pi satisfying the condition sinx=
`√(2) /2`

Answer 1

x = π/4 (45°)

x = 3π/4 (135°)

Explanation:

Find the basic angle α:

α = sin⁻¹(√2/2)

α = π/4

Since, the sine function is positive in the first and second quadrants our values of x will be α and π-α.

So, the angles where 0 ≤ x ≤ 2π satisfying sin(x) = √2/2 are:

x = π/4 (45°)

x = 3π/4 (135°)