What is the general solution for sin^2(x)+3sin(x)=-2 ?

The general solution for sin^2(x)+3sin(x)=-2 is x=(3pi)/2+2pin

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sin^2(x)+3sin(x)=-2

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

x = \frac{3 π}{2} + 2 πn

Solution steps

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

Solve by substitution

sin (x) = - 1, sin (x) = - 2

sin (x) = - 1 : x = \frac{3 π}{2} + 2 πn

sin (x) = - 2 :

No Solution

Combine all the solutions

x = \frac{3 π}{2} + 2 πn

- sin (π x) π = 0

cos^{2} (x) - 3 sin^{2} (x) = 1

sin (\frac{x}{6}) = 0

(tan (θ) - 1) (sec (θ) - 1) = 0, 0 \leq θ \leq 2 π

cos (θ) = \frac{4.4}{11}

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