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

Problem

2*sin(x)+√(,3)=0

Solution

1. Isolate the sine term by subtracting √(,3) from 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 by finding the value in the first quadrant where sin(θ)=√(,3)/2

θ=π/3

4. Determine the quadrants where the sine function is negative, which are Quadrant III and Quadrant IV.

x=π+π/3=(4*π)/3

x=2*π−π/3=(5*π)/3

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

x=(4*π)/3+2*k*π

x=(5*π)/3+2*k*π

Final Answer

x=(4*π)/3+2*k*π,(5*π)/3+2*k*π

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