# Solve for x tan(x)=-2

Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Evaluate .
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 the expression to find the second solution.
Simplify .
Multiply by .
Subtract from .
The resulting angle of is positive and coterminal with .
Find the period.
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 every negative angle to get positive angles.
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
Solve for x tan(x)=-2