What is the general solution for -2sin^2(θ)+5sin(θ)=2 ?

The general solution for -2sin^2(θ)+5sin(θ)=2 is θ= pi/6+2pin,θ=(5pi)/6+2pin

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-2sin^2(θ)+5sin(θ)=2

- 2 sin^{2} (θ) + 5 sin (θ) = 2

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Solution steps

- 2 sin^{2} (θ) + 5 sin (θ) = 2

Solve by substitution

sin (θ) = \frac{1}{2}, sin (θ) = 2

sin (θ) = \frac{1}{2} : θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

sin (θ) = 2 :

No Solution

Combine all the solutions

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

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

3 sin (x) - 2 = 0

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

tan (x) = \frac{3 3}{5}

tan (x) + 1 = - \frac{1}{3} - \frac{1}{3} cot (x)

What is the general solution for -2sin^2(θ)+5sin(θ)=2 ?
The general solution for -2sin^2(θ)+5sin(θ)=2 is θ= pi/6+2pin,θ=(5pi)/6+2pin