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

The general solution for 2sin(2(x-pi/3))=-sqrt(3) is x=pin+pi,x=pin+(7pi)/6

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

2 sin (2 (x - \frac{π}{3})) = - 3

x = πn + π, x = πn + \frac{7 π}{6}

Solution steps

2 sin (2 (x - \frac{π}{3})) = - 3

Divide both sides by

2

sin (2 (x - \frac{π}{3})) = - \frac{3}{2}

General solutions for

sin (2 (x - \frac{π}{3})) = - \frac{3}{2}

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

Solve

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

Solve

2 (x - \frac{π}{3}) = \frac{5 π}{3} + 2 πn : x = πn + \frac{7 π}{6}

x = πn + π, x = πn + \frac{7 π}{6}

- 6 sin (x) - 6 cos (x) = 0

sin (4 x) - sin (2 x) = cos (3 x)

sin (x) = 0.7392

sin (2 x) sec (x) + 2 cos (x) = 0

3 + 2 sin (x) = 0

What is the general solution for 2sin(2(x-pi/3))=-sqrt(3) ?
The general solution for 2sin(2(x-pi/3))=-sqrt(3) is x=pin+pi,x=pin+(7pi)/6