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# Trigonometry Examples

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

Rewrite the equation as .

Subtract from 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 .

Move the negative in front of the fraction.

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

Evaluate .

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 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.

Multiply by .

Subtract from .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Divide by .

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 .

Cancel the common factor of .

Cancel the common factor.

Divide by .

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

, 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 .

Add and .

These are the and intercepts of the equation .

x-intercept: , for any integer

y-intercept: