Solve for x 2cos(x)+ square root of 3=0

Problem

2*cos(x)+√(,3)=0

Solution

1. Isolate the trigonometric term by subtracting √(,3) from both sides of the equation.

2*cos(x)=−√(,3)

2. Divide both sides by 2 to solve for cos(x)

cos(x)=−√(,3)/2

3. Identify the reference angle by finding the value in the first quadrant where the cosine is √(,3)/2

(x_ref)=π/6

4. Determine the quadrants where the cosine function is negative, which are Quadrant II and Quadrant III.

x=π−π/6=(5*π)/6

x=π+π/6=(7*π)/6

5. Generalize the solution by adding multiples of the period 2*π to account for all possible values of x where n is any integer.

x=(5*π)/6+2*n*π

x=(7*π)/6+2*n*π

Final Answer

x=(5*π)/6+2*n*π,(7*π)/6+2*n*π

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