Solve for x cos(x)=2/3

Problem

cos(x)=2/3

Solution

1. Identify the equation as a basic trigonometric equation where the cosine of an angle x is equal to a constant k

2. Apply the inverse cosine function to both sides of the equation to find the principal value of x

x=arccos(2/3)

3. Determine the general solution for cosine, which accounts for the periodicity of 2*π and the symmetry of the cosine function about the x-axis (cos(x)=cos(−x).

x=±arccos(2/3)+2*π*n

4. Specify the domain for the integer constant n which represents any integer.

n∈ℤ

Final Answer

cos(x)=2/3⇒x=±arccos(2/3)+2*π*n,n∈ℤ

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