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# Trigonometry Examples

Isolate to the left side of the equation.

Rewrite the equation as .

Multiply both sides of the equation by .

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of .

Move the leading negative in into the numerator.

Move the leading negative in into the numerator.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply.

Multiply by .

Multiply by .

Simplify .

Combine and .

Move to the left of .

Complete the square for .

Use the form , to find the values of , , and .

Consider the vertex form of a parabola.

Substitute the values of and into the formula .

Simplify the right side.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Cancel the common factor.

Rewrite the expression.

Multiply the numerator by the reciprocal of the denominator.

Multiply .

Multiply by .

Multiply by .

Find the value of using the formula .

Simplify each term.

Raising to any positive power yields .

Simplify the denominator.

Multiply by .

Combine and .

Multiply by .

Move the negative in front of the fraction.

Multiply the numerator by the reciprocal of the denominator.

Multiply .

Multiply by .

Multiply by .

Multiply by .

Add and .

Substitute the values of , , and into the vertex form .

Set equal to the new right side.

Use the vertex form, , to determine the values of , , and .

Find the vertex .