Solve for x cos(4x)=0

Problem

cos(4*x)=0

Solution

1. Identify the general solution for the cosine function where the output is zero.

cos(θ)=0⇒θ=π/2+n*π

2. Substitute the argument of the cosine function, 4*x into the general solution formula, where n is any integer.

4*x=π/2+n*π

3. Isolate the variable x by dividing both sides of the equation by 4

x=(π/2+n*π)/4

4. Simplify the expression to find the final general solution for x

x=π/8+(n*π)/4

Final Answer

cos(4*x)=0⇒x=π/8+(n*π)/4,n∈ℤ

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