What is the general solution for 2sin(x-pi/3)+sqrt(3)=0 ?

The general solution for 2sin(x-pi/3)+sqrt(3)=0 is x=2pin+(5pi)/3 ,x=2pin+2pi

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2sin(x-pi/3)+sqrt(3)=0

2 sin (x - \frac{π}{3}) + 3 = 0

x = 2 πn + \frac{5 π}{3}, x = 2 πn + 2 π

Solution steps

2 sin (x - \frac{π}{3}) + 3 = 0

Move

3

to the right side

2 sin (x - \frac{π}{3}) = - 3

Divide both sides by

2

sin (x - \frac{π}{3}) = - \frac{3}{2}

General solutions for

sin (x - \frac{π}{3}) = - \frac{3}{2}

x - \frac{π}{3} = \frac{4 π}{3} + 2 πn, x - \frac{π}{3} = \frac{5 π}{3} + 2 πn

Solve

x - \frac{π}{3} = \frac{4 π}{3} + 2 πn : x = 2 πn + \frac{5 π}{3}

Solve

x - \frac{π}{3} = \frac{5 π}{3} + 2 πn : x = 2 πn + 2 π

x = 2 πn + \frac{5 π}{3}, x = 2 πn + 2 π

sin (x) = 0.77

sin (x) = 0.87

sin (x) = 0.14

sin (x) = 0.41

sin (x) = 0.39

What is the general solution for 2sin(x-pi/3)+sqrt(3)=0 ?
The general solution for 2sin(x-pi/3)+sqrt(3)=0 is x=2pin+(5pi)/3 ,x=2pin+2pi