What is the general solution for 2sin(3x-pi/6)+sqrt(3)=0 ?

The general solution for 2sin(3x-pi/6)+sqrt(3)=0 is x=(2pin)/3+pi/2 ,x=(2pin)/3+(11pi)/(18)

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2sin(3x-pi/6)+sqrt(3)=0

2 sin (3 x - \frac{π}{6}) + 3 = 0

x = \frac{2 πn}{3} + \frac{π}{2}, x = \frac{2 πn}{3} + \frac{11 π}{18}

Solution steps

2 sin (3 x - \frac{π}{6}) + 3 = 0

Move

3

to the right side

2 sin (3 x - \frac{π}{6}) = - 3

Divide both sides by

2

sin (3 x - \frac{π}{6}) = - \frac{3}{2}

General solutions for

sin (3 x - \frac{π}{6}) = - \frac{3}{2}

3 x - \frac{π}{6} = \frac{4 π}{3} + 2 πn, 3 x - \frac{π}{6} = \frac{5 π}{3} + 2 πn

Solve

3 x - \frac{π}{6} = \frac{4 π}{3} + 2 πn : x = \frac{2 πn}{3} + \frac{π}{2}

Solve

3 x - \frac{π}{6} = \frac{5 π}{3} + 2 πn : x = \frac{2 πn}{3} + \frac{11 π}{18}

x = \frac{2 πn}{3} + \frac{π}{2}, x = \frac{2 πn}{3} + \frac{11 π}{18}

1 2^{2} = 1 0^{2} + 1 2^{2} - 2 (10) (12) cos (b)

x, sin (t) - csc (x) + 1 = 0

tan^{2} (x) = sec^{2} (x) + 1

12 = 3 sec (θ) + 5 csc (θ)

tan^{2} (4 (x + \frac{π}{2})) = 3

What is the general solution for 2sin(3x-pi/6)+sqrt(3)=0 ?
The general solution for 2sin(3x-pi/6)+sqrt(3)=0 is x=(2pin)/3+pi/2 ,x=(2pin)/3+(11pi)/(18)