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

The general solution for 2sin^2(θ)-5sin(θ)=3 is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin

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2sin^2(θ)-5sin(θ)=3

2 sin^{2} (θ) - 5 sin (θ) = 3

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

Solution steps

2 sin^{2} (θ) - 5 sin (θ) = 3

Solve by substitution

sin (θ) = 3, sin (θ) = - \frac{1}{2}

sin (θ) = 3 :

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

cos (3 x - \frac{π}{4}) = \frac{1}{2}, 0 \leq x \leq π

4 sin^{2} (x) = 3, 0 \leq x \leq 10 8^{\circ}

3 sin (x) + 3 cos (x) = 0

4 sin (2 x) + 4 cos (x) = 0

2 + cos (2 x) + 3 cos (x) = 0

What is the general solution for 2sin^2(θ)-5sin(θ)=3 ?
The general solution for 2sin^2(θ)-5sin(θ)=3 is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin