Solve for x 2sin(x)- square root of 3=0

Problem

2*sin(x)−√(,3)=0

Solution

1. Isolate the sine term by adding √(,3) to both sides of the equation.

2*sin(x)=√(,3)

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

sin(x)=√(,3)/2

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

x=π/3

4. Determine all solutions within the interval [0,2*π) by finding the angles in the quadrants where sine is positive (Quadrants I and II).

x=π/3

x=π−π/3=(2*π)/3

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

x=π/3+2*n*π

x=(2*π)/3+2*n*π

Final Answer

x=π/3+2*n*π,(2*π)/3+2*n*π

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