,

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

Evaluate .

Multiply each term in by .

Multiply .

Multiply by .

Multiply by .

Multiply by .

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.

Add and .

Multiply each term in by

Multiply each term in by .

Multiply .

Multiply by .

Multiply by .

Multiply by .

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.

Replace with decimal approximation.

Subtract from .

List the new angles.

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

, for any integer

Exclude the solutions that do not make true.

, for any integer

Take the base solution.

Replace the variable with in the expression.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Evaluate tan(-x)=1/4 , sec(x)