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# Precalculus Examples

Step 1

Divide each term in the equation by .

Step 2

Convert from to .

Step 3

Step 3.1

Cancel the common factor.

Step 3.2

Rewrite the expression.

Step 4

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

Step 5

Step 5.1

The exact value of is .

Step 6

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

Step 7

Step 7.1

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

Step 7.2

Combine fractions.

Step 7.2.1

Combine and .

Step 7.2.2

Combine the numerators over the common denominator.

Step 7.3

Simplify the numerator.

Step 7.3.1

Move to the left of .

Step 7.3.2

Add and .

Step 8

Step 8.1

The period of the function can be calculated using .

Step 8.2

Replace with in the formula for period.

Step 8.3

The absolute value is the distance between a number and zero. The distance between and is .

Step 8.4

Divide by .

Step 9

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

, for any integer

Step 10

Consolidate the answers.

, for any integer