Solve for x sin(3x)=0

Problem

sin(3*x)=0

Solution

1. Identify the general solution for the sine function where the output is zero. The equation sin(θ)=0 occurs when the angle is an integer multiple of π

θ=n*π

where n is any integer (n∈ℤ.

2. Substitute the argument of the sine function, which is 3*x into the general solution formula.

3*x=n*π

3. Isolate the variable x by dividing both sides of the equation by 3.

x=(n*π)/3

Final Answer

sin(3*x)=0⇒x=(n*π)/3,n∈ℤ

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