What is the general solution for 2sin^2(θ)-7sin(θ)-4=0 ?

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

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2sin^2(θ)-7sin(θ)-4=0

2 sin^{2} (θ) - 7 sin (θ) - 4 = 0

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

Solution steps

2 sin^{2} (θ) - 7 sin (θ) - 4 = 0

Solve by substitution

sin (θ) = 4, sin (θ) = - \frac{1}{2}

sin (θ) = 4 :

No Solution

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

Combine all the solutions

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

2 tan (x) - 23 = 0

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

2 sin^{2} (\frac{x}{4}) - 3 cos (\frac{x}{4}) = 0

cos^{2} (A) + sin^{2} (A) = \frac{1}{sin ^{2} ( A )}

cos (4 θ) = 1

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