# Solve for x tan(x) plus square root of three equals zero

Subtract from both sides of the equation.

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

The exact value of is .

The tangent function is negative in the second and fourth quadrants. To calculate the second answer, subtract the reference angle from to find the solution in the third quadrant.

Clarify .

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

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Add.

Multiply by .

Add numerators over the common denominator.

Clarify the numerator.

Multiply by .

Subtract from .

Put the negative in front of the fraction.

Add to .

The resulting angle of is positive and coterminal with .

Evaluate the period of function using .

Replace with in the formula for period.

Find solution to the equation.

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

First, divide by .

Add to to find the positive angle.

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

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Put to the left of .

Subtract from .

Write the new angles.

The period of the function is so values will repeat every radians in two directions at once.

, for any integer

Consolidate the answers.

, for any integer

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