# Trigonometry Examples

Since contains the variable to solve for, move it to the left side of the equation by subtracting from both sides.

Subtract from to get .

Divide each term in by .

Simplify the left side of the equation by cancelling the common factors.

Reduce the expression by cancelling the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move the negative one from the denominator of .

Simplify the expression.

Multiply by to get .

Rewrite as .

Move the negative in front of the fraction.

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

The exact value of is .

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.

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 to get .

Combine the numerators over the common denominator.

Simplify each term.

Simplify the numerator.

Factor out of .

Multiply by to get .

Add and to get .

Move to the left of the expression .

Multiply by to get .

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 to get .

Combine the numerators over the common denominator.

Simplify the numerator.

Move to the left of the expression .

Multiply by to get .

Add and to get .

Subtract from .

The resulting angle of is positive, less than , and coterminal with .

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 to get .

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.

Multiply by to get .

Combine the numerators over the common denominator.

Simplify the numerator.

Factor out of .

Multiply by to get .

Subtract from to get .

Simplify the expression.

Move to the left of the expression .

Multiply by to get .

List the new angles.

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