What is the general solution for solvefor x,1+2sin(x)=0 ?

The general solution for solvefor x,1+2sin(x)=0 is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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solvefor x,1+2sin(x)=0

solve for

x, 1 + 2 sin (x) = 0

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

Solution steps

1 + 2 sin (x) = 0

Move

1

to the right side

2 sin (x) = - 1

Divide both sides by

2

sin (x) = - \frac{1}{2}

General solutions for

sin (x) = - \frac{1}{2}

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

sin (x) = \frac{- 5}{13}

sin^{2} (θ) - cos^{2} (θ) + cos (θ) = 0

3 sin^{2} (x) = 9 cos^{2} (x)

sin (\frac{1}{2 x}) = - 1

3 cos^{2} (x) - 3 = sin (x)

What is the general solution for solvefor x,1+2sin(x)=0 ?
The general solution for solvefor x,1+2sin(x)=0 is x=(7pi)/6+2pin,x=(11pi)/6+2pin