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 radians, π radians, 2*π radians, and so on.

3. Generalize the solution to include all possible rotations. Since the sine function is periodic with a period of 2*π and the zeros occur every π radians, the solutions can be expressed using an integer n

4. State the solution set where n is any integer (n∈ℤ.

Final Answer

sin(x)=0⇒x=n*π

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