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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 .

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

Evaluate .

Move all terms not containing to the right side of the equation.

Add to both sides of the equation.

Simplify the right side of the equation.

Replace with decimal approximation.

Add and .

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

Simplify the expression to find the second solution.

Subtract from .

Move all terms not containing to the right side of the equation.

Add to both sides of the equation.

Simplify the right side of the equation.

Replace with decimal approximation.

Add and .

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 .

Subtract from .

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

The exact value of is .

Multiply by .

Subtract from .

These are the and intercepts of the equation .

x-intercept: , for any integer

y-intercept: