What is the general solution for -4sin^2(θ)-3sin(θ)+5=0 ?

The general solution for -4sin^2(θ)-3sin(θ)+5=0 is θ=0.93440…+2pin,θ=pi-0.93440…+2pin

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-4sin^2(θ)-3sin(θ)+5=0

- 4 sin^{2} (θ) - 3 sin (θ) + 5 = 0

θ = 0.93440 \dots + 2 πn, θ = π - 0.93440 \dots + 2 πn

Solution steps

- 4 sin^{2} (θ) - 3 sin (θ) + 5 = 0

Solve by substitution

sin (θ) = - \frac{3 + 89}{8}, sin (θ) = \frac{89 - 3}{8}

sin (θ) = - \frac{3 + 89}{8} :

No Solution

sin (θ) = \frac{89 - 3}{8} : θ = arcsin (\frac{89 - 3}{8}) + 2 πn, θ = π - arcsin (\frac{89 - 3}{8}) + 2 πn

Combine all the solutions

θ = arcsin (\frac{89 - 3}{8}) + 2 πn, θ = π - arcsin (\frac{89 - 3}{8}) + 2 πn

Show solutions in decimal form

θ = 0.93440 \dots + 2 πn, θ = π - 0.93440 \dots + 2 πn

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

cos (θ) + 2 cos (θ + 24 0^{\circ}) = 1

arccos (x) = \frac{π}{8}

sin (θ) = 5

sin^{2} (x) = 4 cos (x)

What is the general solution for -4sin^2(θ)-3sin(θ)+5=0 ?
The general solution for -4sin^2(θ)-3sin(θ)+5=0 is θ=0.93440…+2pin,θ=pi-0.93440…+2pin