# Trigonometry Examples

Step 1

Add to both sides of the equation.

Step 2

Divide each term in by .

Simplify the left side.

Cancel the common factor of .

Cancel the common factor.

Divide by .

Step 3

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

Step 4

The exact value of is .

Step 5

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.

Step 6

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

Combine fractions.

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Subtract from .

Step 7

The period of the function can be calculated using .

Replace with in the formula for period.

The absolute value is the distance between a number and zero. The distance between and is .

Divide by .

Step 8

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

, for any integer