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

The general solution for -7sin^2(θ)+4sin(θ)+7=0 is θ=-0.85458…+2pin,θ=pi+0.85458…+2pin

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-7sin^2(θ)+4sin(θ)+7=0

- 7 sin^{2} (θ) + 4 sin (θ) + 7 = 0

θ = - 0.85458 \dots + 2 πn, θ = π + 0.85458 \dots + 2 πn

Solution steps

- 7 sin^{2} (θ) + 4 sin (θ) + 7 = 0

Solve by substitution

sin (θ) = - \frac{- 2 + 53}{7}, sin (θ) = \frac{2 + 53}{7}

sin (θ) = - \frac{- 2 + 53}{7} : θ = arcsin (- \frac{- 2 + 53}{7}) + 2 πn, θ = π + arcsin (\frac{- 2 + 53}{7}) + 2 πn

sin (θ) = \frac{2 + 53}{7} :

No Solution

Combine all the solutions

θ = arcsin (- \frac{- 2 + 53}{7}) + 2 πn, θ = π + arcsin (\frac{- 2 + 53}{7}) + 2 πn

Show solutions in decimal form

θ = - 0.85458 \dots + 2 πn, θ = π + 0.85458 \dots + 2 πn

- 2 sin^{2} (x) = - 3 sin (x) + 1

sin (x) = \frac{6}{10}

sin (3 x) = 3 cos (3 x)

(9 sin (2 x) + 9 cos (2 x))^{2} = 81

- 2 cos^{2} (θ) + sin (θ) - 3 = - 4

What is the general solution for -7sin^2(θ)+4sin(θ)+7=0 ?
The general solution for -7sin^2(θ)+4sin(θ)+7=0 is θ=-0.85458…+2pin,θ=pi+0.85458…+2pin