Solve for x cot(x)=-1

Problem

cot(x)=−1

Solution

1. Rewrite the equation using the tangent function, since cot(x)=1/tan(x)

tan(x)=−1

2. Identify the reference angle by finding the value of x in the first quadrant where tan(x)=1

(x_ref)=π/4

3. Determine the quadrants where the tangent function is negative, which are Quadrant II and Quadrant IV.

x=π−π/4=(3*π)/4

x=2*π−π/4=(7*π)/4

4. Generalize the solution by adding the period of the tangent function, which is π where n is any integer.

x=(3*π)/4+n*π

Final Answer

cot(x)=−1⇒x=(3*π)/4+n*π

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