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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

The exact value of is .

Step 3

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.

Step 4

Add to .

The resulting angle of is positive and coterminal with .

Step 5

The period of the function can be calculated using .

Replace with in the formula for period.

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

Divide by .

Step 6

Add to to find the positive angle.

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

Combine fractions.

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Move to the left of .

Subtract from .

List the new angles.

Step 7

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

, for any integer

Step 8

Consolidate the answers.

, for any integer