# Trigonometry Examples

Since does not contain the variable to solve for, move it to the right side of the equation by adding to both sides.

Divide each term in by .

Reduce the expression by cancelling the common factors.

Cancel the common factor.

Divide by to get .

Take the square root of both sides of the equation to eliminate the exponent on the left side.

Simplify the right side of the equation.

Rewrite using the quotient rule for radicals.

Any root of is .

Simplify the denominator.

Rewrite as .

Pull terms out from under the radical, assuming positive real numbers.

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the to find the first solution.

Next, use the negative value of the to find the second solution.

The complete solution is the result of both the positive and negative portions of the solution.

Set up each of the solutions to solve for .

Set up the equation to solve for .

Simplify the expression to find the first solution.

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

The exact value of is .

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

Simplify the expression to find the second solution.

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 .

Find the period.

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 .

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

Set up the equation to solve for .

Simplify the expression to find the first solution.

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

The exact value of is .

The cosine function is negative in the second and third quadrants. To find the second solution, subtract the reference angle from to find the solution in the third quadrant.

Simplify the expression to find the second solution.

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 .

Multiply by to get .

Multiply by to get .

Subtract from to get .

Simplify the expression.

Move to the left of the expression .

Multiply by to get .

Find the period.

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 .

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

List all of the results found in the previous steps.

The complete solution is the set of all solutions.