# Solve for x cos(x)=sin(x)

Divide each term in the equation by .

Cancel the common factor.

Divide by .

Convert from to .

Rewrite the equation as .

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 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.

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.

Move to the left of .

Add and .

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 .

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

, for any integer

Consolidate the answers.

, for any integer

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