Take the inverse sine of both sides of the equation to extract from inside the sine.

Evaluate .

The sine function is negative in the third and fourth quadrants. To find the second solution, subtract the solution from , to find a reference angle. Next, add this reference angle to to find the solution in the third quadrant.

Remove the parentheses around the expression .

Simplify .

Multiply by .

Add and .

Add and .

The period of the function can be calculated using .

Replace with in the formula for period.

Solve the equation.

The absolute value is the distance between a number and zero. The distance between and is .

Divide by .

Add to to find the positive angle.

Subtract from .

List the new angles.

The period of the function is so values will repeat every radians in both directions.

, for any integer

Solve for ? sin(x)=-0.4