What is the general solution for 2sin(x-pi/6)+1=0 ?

The general solution for 2sin(x-pi/6)+1=0 is x=2pin+(4pi)/3 ,x=2pin+2pi

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2sin(x-pi/6)+1=0

2 sin (x - \frac{π}{6}) + 1 = 0

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

Solution steps

2 sin (x - \frac{π}{6}) + 1 = 0

Move

1

to the right side

2 sin (x - \frac{π}{6}) = - 1

Divide both sides by

2

sin (x - \frac{π}{6}) = - \frac{1}{2}

General solutions for

sin (x - \frac{π}{6}) = - \frac{1}{2}

x - \frac{π}{6} = \frac{7 π}{6} + 2 πn, x - \frac{π}{6} = \frac{11 π}{6} + 2 πn

Solve

x - \frac{π}{6} = \frac{7 π}{6} + 2 πn : x = 2 πn + \frac{4 π}{3}

Solve

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

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

3 - 3 sin (θ) = 6 cos^{2} (θ)

sin (x) + sin^{2} (x) + cos^{2} (x) = 1

tan (3 x) = 5 tan (x)

2 cos (2 x) - 2 = 0

3 tan^{2} (x) + 4 sec (x) = - 4

What is the general solution for 2sin(x-pi/6)+1=0 ?
The general solution for 2sin(x-pi/6)+1=0 is x=2pin+(4pi)/3 ,x=2pin+2pi