What is the general solution for -3sin^2(θ)+5sin(θ)-1=1 ?

The general solution for -3sin^2(θ)+5sin(θ)-1=1 is θ=0.72972…+2pin,θ=pi-0.72972…+2pin,θ= pi/2+2pin

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-3sin^2(θ)+5sin(θ)-1=1

- 3 sin^{2} (θ) + 5 sin (θ) - 1 = 1

θ = 0.72972 \dots + 2 πn, θ = π - 0.72972 \dots + 2 πn, θ = \frac{π}{2} + 2 πn

Solution steps

- 3 sin^{2} (θ) + 5 sin (θ) - 1 = 1

Solve by substitution

sin (θ) = \frac{2}{3}, sin (θ) = 1

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

sin (θ) = 1 : θ = \frac{π}{2} + 2 πn

Combine all the solutions

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

Show solutions in decimal form

θ = 0.72972 \dots + 2 πn, θ = π - 0.72972 \dots + 2 πn, θ = \frac{π}{2} + 2 πn

14 sin^{2} (x) + 21 sin (x) + 7 = 0

2 sec (θ) + 6 = 10

2 sin^{2} (θ) = 3 sin (θ) - 1

cot (θ) = - 5

2 + 2 sin (x) = 0

What is the general solution for -3sin^2(θ)+5sin(θ)-1=1 ?
The general solution for -3sin^2(θ)+5sin(θ)-1=1 is θ=0.72972…+2pin,θ=pi-0.72972…+2pin,θ= pi/2+2pin