# Solve for ? sin(two x) equals minus one First, divide two

Solve for ? sin(2x)=-1/2
Take the inverse sine of both sides of the equation to extract from inside the sine.
The exact value of is .
Divide each term by and simplify.
Divide each term in by .
The common factor should be canceled of .
Cancel the common factor.
Divide by .
First, multiply .
Multiply and .
First, multiply by .
The sine function is negative in the third and fourth quadrants. To calculate the second answer, subtract the solution from , to find a reference angle. Next, add this reference angle to to find the solution in the third quadrant.
Clarify the expression To calculate the second answer.
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 .
Multiply by .
Add numerators over the common denominator.
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.
Multiply by .
Divide each term by and simplify.
Divide each term in by .
The common factor should be canceled.
Cancel the common factor.
Divide by .
Multiply .
Multiply and .
Multiply by .
Calculate the period.
Evaluate the period of function using .
Replace with in the formula for period.
Find solution to 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 .
Add to every negative angle to get positive angles.
Add to to find the positive angle.
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.
First, multiply by .
Combine the numerators over the common denominator.
Clarify the numerator.
Move to the left of .
Subtract from .
Write the new angles.
The period of the function is so values will repeat every radians in two directions at once.
, for any integer
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