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. Rewrite the equation to find where the ratio of cosine to sine equals 1.

cos(x)/sin(x)=1

3. Rearrange the equation by multiplying both sides by sin(x)

cos(x)=sin(x)

4. Determine the values of x within the unit circle where the sine and cosine values are identical.

x=π/4

x=(5*π)/4

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

x=π/4+n*π

Final Answer

cot(x)=1⇒x=π/4+n*π

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