What is the general solution for 6sin^2(x)+9sin(x)+3=0 ?

The general solution for 6sin^2(x)+9sin(x)+3=0 is x=(7pi)/6+2pin,x=(11pi)/6+2pin,x=(3pi)/2+2pin

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6sin^2(x)+9sin(x)+3=0

6 sin^{2} (x) + 9 sin (x) + 3 = 0

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

6 sin^{2} (x) + 9 sin (x) + 3 = 0

Solve by substitution

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

sin (x) = - \frac{1}{2} : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

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

Combine all the solutions

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{3 π}{2} + 2 πn

cos^{2} (x) + 2 cos (x) - 1 = 0

tan (θ) = 0.1

1 - 2 sin^{2} (x) = 0

8 sin^{2} (θ) = 6

72 sin^{2} (x) = 72 - 36 cos (x)

What is the general solution for 6sin^2(x)+9sin(x)+3=0 ?
The general solution for 6sin^2(x)+9sin(x)+3=0 is x=(7pi)/6+2pin,x=(11pi)/6+2pin,x=(3pi)/2+2pin