Solve for x sin(x)=0

Problem

sin(x)=0

Solution

1. Identify the zeros of the sine function on the unit circle. The sine of an angle represents the y-coordinate of a point on the unit circle.

2. Determine the angles where the y-coordinate is zero. This occurs at the horizontal axis, specifically at 0 and π radians.

3. Generalize the solution to include all possible rotations. Since the sine function is periodic with a period of 2*π the solutions occur at every integer multiple of π

4. Express the solution using an integer variable n where n represents any integer in the set {...,−2,−1,0,1,2,...}

Final Answer

sin(x)=0⇒x=n*π,n∈ℤ

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