Solve for x sin(5x)=0

Problem

sin(5*x)=0

Solution

1. Identify the general solution for the sine function. The equation sin(θ)=0 is satisfied when the argument is an integer multiple of π

θ=n*π

where n is any integer (n∈ℤ.

2. Substitute the argument of the given function into the general solution.

5*x=n*π

3. Isolate the variable x by dividing both sides of the equation by 5

x=(n*π)/5

Final Answer

sin(5*x)=0⇒x=(n*π)/5,n∈ℤ

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