What is the general solution for 2sin(x+pi/9)=-1 ?

The general solution for 2sin(x+pi/9)=-1 is x=2pin+(19pi)/(18),x=2pin+(31pi)/(18)

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2sin(x+pi/9)=-1

2 sin (x + \frac{π}{9}) = - 1

x = 2 πn + \frac{19 π}{18}, x = 2 πn + \frac{31 π}{18}

Solution steps

2 sin (x + \frac{π}{9}) = - 1

Divide both sides by

2

sin (x + \frac{π}{9}) = - \frac{1}{2}

General solutions for

sin (x + \frac{π}{9}) = - \frac{1}{2}

x + \frac{π}{9} = \frac{7 π}{6} + 2 πn, x + \frac{π}{9} = \frac{11 π}{6} + 2 πn

Solve

x + \frac{π}{9} = \frac{7 π}{6} + 2 πn : x = 2 πn + \frac{19 π}{18}

Solve

x + \frac{π}{9} = \frac{11 π}{6} + 2 πn : x = 2 πn + \frac{31 π}{18}

x = 2 πn + \frac{19 π}{18}, x = 2 πn + \frac{31 π}{18}

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What is the general solution for 2sin(x+pi/9)=-1 ?
The general solution for 2sin(x+pi/9)=-1 is x=2pin+(19pi)/(18),x=2pin+(31pi)/(18)