What is the general solution for 4sin^2(x)+6sin(x)+2=0 ?

The general solution for 4sin^2(x)+6sin(x)+2=0 is x=(7pi)/6+2pin,x=(11pi)/6+2pin,x=(3pi)/2+2pin

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4sin^2(x)+6sin(x)+2=0

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

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

Solution steps

4 sin^{2} (x) + 6 sin (x) + 2 = 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

sin^{2} (θ) + 2 - cos^{2} (θ) = 3 sin (θ)

sin (x) = sin^{2} (x)

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

tan^{2} (x) + 2 tan (x) + 1 = 0

sin^{2} (x) + sin (x) cos (x) = 0

What is the general solution for 4sin^2(x)+6sin(x)+2=0 ?
The general solution for 4sin^2(x)+6sin(x)+2=0 is x=(7pi)/6+2pin,x=(11pi)/6+2pin,x=(3pi)/2+2pin