Solve for x 2cos(x)=1

Problem

2*cos(x)=1

Solution

1. Isolate the trigonometric function by dividing both sides of the equation by 2

2*cos(x)=1

cos(x)=1/2

2. Identify the reference angle in the first quadrant where the cosine value is 1/2

cos(π/3)=1/2

3. Determine the general solutions for x by considering the quadrants where cosine is positive (Quadrant I and Quadrant IV) and the periodicity of the cosine function.

x=π/3+2*n*π

x=−π/3+2*n*π

4. Combine the solutions into a standard form where n is any integer.

x=±π/3+2*n*π

Final Answer

x=±π/3+2*n*π,n∈ℤ

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