Solve for x 2cos(x) = square root of 3

Problem

2*cos(x)=√(,3)

Solution

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

cos(x)=√(,3)/2

2. Identify the reference angle by determining which angle has a cosine value of √(,3)/2

(x_ref)=π/6

3. Determine the quadrants where the cosine function is positive, which are Quadrant I and Quadrant IV.

x=π/6+2*π*n

x=2*π−π/6+2*π*n

4. Simplify the expression for the angle in Quadrant IV.

x=(11*π)/6+2*π*n

5. Generalize the solution for all real numbers where n is any integer.

x=π/6+2*π*n,(11*π)/6+2*π*n

Final Answer

x=π/6+2*π*n,(11*π)/6+2*π*n

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