What is the general solution for 2sin^2(θ)+5sin(θ)=3 ?

The general solution for 2sin^2(θ)+5sin(θ)=3 is θ= pi/6+2pin,θ=(5pi)/6+2pin

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2sin^2(θ)+5sin(θ)=3

2 sin^{2} (θ) + 5 sin (θ) = 3

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

Solution steps

2 sin^{2} (θ) + 5 sin (θ) = 3

Solve by substitution

sin (θ) = \frac{1}{2}, sin (θ) = - 3

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

sin (θ) = - 3 :

No Solution

Combine all the solutions

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

- 4 tan^{2} (θ) - 9 tan (θ) - 2 = 0

3 cos (θ) - 2 = 0

csc^{2} (\frac{x}{2}) + csc (\frac{x}{2}) = 4 + 4 sin (\frac{x}{2})

(cot (x) - 1) (sin (x) + 1) = 0

3 cos (x) = sin (x) + 1

What is the general solution for 2sin^2(θ)+5sin(θ)=3 ?
The general solution for 2sin^2(θ)+5sin(θ)=3 is θ= pi/6+2pin,θ=(5pi)/6+2pin