What is the general solution for 2sin^2(w)+3sin(w)+1=0 ?

The general solution for 2sin^2(w)+3sin(w)+1=0 is w=(7pi)/6+2pin,w=(11pi)/6+2pin,w=(3pi)/2+2pin

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2sin^2(w)+3sin(w)+1=0

2 sin^{2} (w) + 3 sin (w) + 1 = 0

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

Solution steps

2 sin^{2} (w) + 3 sin (w) + 1 = 0

Solve by substitution

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

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

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

Combine all the solutions

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

tan (x) - 2 tan (x) cos (x) = 0

sin (t) cos (t) = cos (t)

- 7 cos (7 x) = 0

1 - 4 sin^{2} (x) = 0

cos (2 θ) - 6 sin^{2} (θ) = - 5

What is the general solution for 2sin^2(w)+3sin(w)+1=0 ?
The general solution for 2sin^2(w)+3sin(w)+1=0 is w=(7pi)/6+2pin,w=(11pi)/6+2pin,w=(3pi)/2+2pin