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

The exact value of is .

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Multiply .

Multiply and .

Multiply by .

The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from to find the solution in the second quadrant.

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Subtract from .

Reorder and .

Subtract from .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Simplify .

Multiply the numerator by the reciprocal of the denominator.

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

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 .

Cancel the common factor of .

Cancel the common factor.

Divide by .

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

, for any integer

Find All Complex Solutions sin(2x)=( square root of 3)/2