Subtract from both sides of the equation.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Move the negative in front of the fraction.

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.

Simplify .

Multiply .

Multiply by .

Combine and .

Move the negative in front of the fraction.

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.

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.

Multiply by .

Add and .

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 .

Add and .

Multiply .

Combine and .

Multiply by .

Subtract from until the angle falls between and . In this case, needs to be subtracted times.

Simplify.

Multiply by .

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.

Multiply by .

Subtract from .

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 .

Add to to find the positive angle.

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

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Subtract from .

List the new angles.

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

, for any integer

Exclude the solutions that do not make true.

, for any integer

Solve for x 2sin(x/4)+ square root of 3=0