# Trigonometry Examples

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

Add and to get .

Divide each term in by .

Reduce the expression by cancelling the common factors.

Cancel the common factor.

Divide by to get .

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.

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 .

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.