Solve for x cos(x)=1/3

Problem

cos(x)=1/3

Solution

1. Identify the equation as a basic trigonometric equation of the form cos(x)=a

2. Apply the inverse cosine function to find the principal value, often called the arccosine.

x=arccos(1/3)

3. Determine the general solution for the cosine function, which accounts for its periodicity of 2*π and its symmetry across the x-axis.

x=±arccos(1/3)+2*n*π

4. Specify the domain of the integer constant used in the general solution.

n∈ℤ

Final Answer

cos(x)=1/3⇒x=±arccos(1/3)+2*n*π,n∈ℤ

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