Solve for x cot(x)=0

Problem

cot(x)=0

Solution

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

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

2. Set the expression equal to zero and recognize that a fraction is zero only when its numerator is zero and its denominator is non-zero.

cos(x)/sin(x)=0

3. Solve for the values of x where the numerator is zero.

cos(x)=0

4. Determine the general solution for x based on the unit circle, where the cosine function equals zero at odd multiples of π/2

x=π/2+n*π

5. Verify that the denominator sin(x) is not zero at these points. Since sin(π/2+n*π)=±1 the expression is defined.

n∈ℤ

Final Answer

cot(x)=0⇒x=π/2+n*π,n∈ℤ

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