# Solve for ? sin(x/2)=1/2

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

The exact value of is .

Multiply both sides of the equation by .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

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.

Multiply both sides of the equation by .

Simplify both sides of the equation.

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Simplify .

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

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Move to the left of .

Subtract from .

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.

is approximately which is positive so remove the absolute value

Multiply the numerator by the reciprocal of the denominator.

Multiply by .

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

, for any integer

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