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# Trigonometry Examples

Divide each term in the equation by .

Factor out of .

Replace with an equivalent expression in the numerator.

Remove parentheses.

Apply the distributive property.

Rewrite in terms of sines and cosines.

Apply the distributive property.

Combine and .

Combine and .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Separate fractions.

Convert from to .

Divide by .

Separate fractions.

Convert from to .

Divide by .

Multiply by .

Subtract from both sides of the inequality.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

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

The exact value of is .

The tangent function is negative in the second and fourth quadrants. To find the second solution, subtract the reference angle from to find the solution in the third quadrant.

Simplify .

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

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Subtract from .

Move the negative in front of the fraction.

Add to .

The resulting angle of is positive and coterminal with .

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 .

Divide by .

Add to to find the positive angle.

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

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Move to the left of .

Subtract from .

List the new angles.

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

, for any integer

Convert the inequality to interval notation.