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# Trigonometry Examples

Step 1

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

Step 2

Step 2.1

The exact value of is .

Step 3

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 4

Step 4.1

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

Step 4.2

Combine fractions.

Step 4.2.1

Combine and .

Step 4.2.2

Combine the numerators over the common denominator.

Step 4.3

Simplify the numerator.

Step 4.3.1

Move to the left of .

Step 4.3.2

Add and .

Step 5

Step 5.1

The period of the function can be calculated using .

Step 5.2

Replace with in the formula for period.

Step 5.3

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

Step 5.4

Divide by .

Step 6

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

, for any integer

Step 7

Consolidate the answers.

, for any integer