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# Trigonometry Examples

To find the x-intercept, substitute in for and solve for .

Rewrite the equation as .

Add to both sides of the equation.

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Divide by .

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

The exact value of is .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Divide by .

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.

Multiply by .

Add and .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Find the period.

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 .

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

, for any integer

Consolidate the answers.

, for any integer

, for any integer

To find the y-intercept, substitute in for and solve for .

Simplify each term.

Multiply by .

The exact value of is .

Multiply by .

Subtract from .

These are the and intercepts of the equation .

x-intercept: , for any integer

y-intercept: