Solve for x cot(x)=-( square root of 3)/3

Problem

cot(x)=−√(,3)/3

Solution

1. Rewrite the equation in terms of the tangent function using the reciprocal identity cot(x)=1/tan(x)

tan(x)=1/(−√(,3)/3)

2. Simplify the fraction by multiplying the numerator by the reciprocal of the denominator.

tan(x)=−3/√(,3)

3. Rationalize the denominator by multiplying the numerator and denominator by √(,3)

tan(x)=−√(,3)

4. Identify the reference angle by finding the value in the first quadrant where tan(θ)=√(,3)

θ=π/3

5. Determine the general solution for x by considering the period of the tangent function, which is π Since the tangent value is negative, the angle lies in the second or fourth quadrant.

x=(2*π)/3+n*π

Final Answer

cot(x)=−√(,3)/3⇒x=(2*π)/3+n*π

Want more problems? Check here!