Solve for x cos(x)=1/2

Problem

cos(x)=1/2

Solution

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

cos(π/3)=1/2

2. Determine the quadrants where the cosine function is positive. Cosine is positive in Quadrant I and Quadrant IV.

(x_1)=π/3

(x_2)=2*π−π/3=(5*π)/3

3. Generalize the solution to include all possible rotations by adding multiples of the period 2*π where n is any integer.

x=π/3+2*n*π

x=(5*π)/3+2*n*π

Final Answer

cos(x)=1/2⇒x=π/3+2*n*π,(5*π)/3+2*n*π

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