Solve for x tan(x)=0

Problem

tan(x)=0

Solution

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

tan(x)=sin(x)/cos(x)

2. Set the expression equal to zero and note that a fraction is zero only when its numerator is zero.

sin(x)/cos(x)=0

sin(x)=0

3. Determine the values of x where the sine function equals zero on the unit circle.

x=0,π,2*π,…

4. Generalize the solution by using an integer k to represent all possible rotations.

x=k*π

Final Answer

tan(x)=0⇒x=k*π,k∈ℤ

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