Solve for x cot(x)=-1

Problem

cot(x)=−1

Solution

1. Identify the definition of the cotangent function in terms of sine and cosine.

cot(x)=cos(x)/sin(x)

2. Set up the equation by substituting the given value.

cos(x)/sin(x)=−1

3. Rearrange the equation to find where the sine and cosine values are opposites.

cos(x)=−sin(x)

4. Determine the reference angle in the first quadrant where |cos(x)|=|sin(x)|

x=π/4

5. Locate the quadrants where the cotangent 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

6. Generalize the solution by adding the period of the cotangent 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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