Question

Find all values of x in the interval [0, 2π] that satisfy the equation.

6sin²(x) = 3

Answer 1

The solutions are π/4, 3π/4,5π/4,7π/4

Explanation:

The given equation is

6sin²(x) = 3

Divide by 6 to get:

`{ \sin}^(2) (x) = (1)/(2)`

This implies that;

`\sin(x) = \pm ( √(2) )/(2)`

If

`\sin(x) = ( √(2) )/(2)`

`x = (\pi)/(4)`

in the first quadrant

`x = (3\pi)/(4)`

in the second quadrant.

If

`\sin(x) = - ( √(2) )/(2)`

`x = (5\pi)/(4)`

in the third quadrant

`x = (7\pi)/(4)`