What is the general solution for -4sin^2(θ)-7sin(θ)+7=0 ?

The general solution for -4sin^2(θ)-7sin(θ)+7=0 is θ=0.79102…+2pin,θ=pi-0.79102…+2pin

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-4sin^2(θ)-7sin(θ)+7=0

- 4 sin^{2} (θ) - 7 sin (θ) + 7 = 0

θ = 0.79102 \dots + 2 πn, θ = π - 0.79102 \dots + 2 πn

Solution steps

- 4 sin^{2} (θ) - 7 sin (θ) + 7 = 0

Solve by substitution

sin (θ) = - \frac{7 + 161}{8}, sin (θ) = \frac{161 - 7}{8}

sin (θ) = - \frac{7 + 161}{8} :

No Solution

sin (θ) = \frac{161 - 7}{8} : θ = arcsin (\frac{161 - 7}{8}) + 2 πn, θ = π - arcsin (\frac{161 - 7}{8}) + 2 πn

Combine all the solutions

θ = arcsin (\frac{161 - 7}{8}) + 2 πn, θ = π - arcsin (\frac{161 - 7}{8}) + 2 πn

Show solutions in decimal form

θ = 0.79102 \dots + 2 πn, θ = π - 0.79102 \dots + 2 πn

2 cos^{2} (4 x) = 1

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

csc^{2} (x) + 3 csc (x) + 2 = 0

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

4.718 tan^{2} (θ) - 13.75 tan (θ) + 8.018 = 0

What is the general solution for -4sin^2(θ)-7sin(θ)+7=0 ?
The general solution for -4sin^2(θ)-7sin(θ)+7=0 is θ=0.79102…+2pin,θ=pi-0.79102…+2pin