What is the general solution for -7sin^2(θ)+4sin(θ)=-3 ?

The general solution for -7sin^2(θ)+4sin(θ)=-3 is θ=-0.44291…+2pin,θ=pi+0.44291…+2pin,θ= pi/2+2pin

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-7sin^2(θ)+4sin(θ)=-3

- 7 sin^{2} (θ) + 4 sin (θ) = - 3

θ = - 0.44291 \dots + 2 πn, θ = π + 0.44291 \dots + 2 πn, θ = \frac{π}{2} + 2 πn

Solution steps

- 7 sin^{2} (θ) + 4 sin (θ) = - 3

Solve by substitution

sin (θ) = - \frac{3}{7}, sin (θ) = 1

sin (θ) = - \frac{3}{7} : θ = arcsin (- \frac{3}{7}) + 2 πn, θ = π + arcsin (\frac{3}{7}) + 2 πn

sin (θ) = 1 : θ = \frac{π}{2} + 2 πn

Combine all the solutions

θ = arcsin (- \frac{3}{7}) + 2 πn, θ = π + arcsin (\frac{3}{7}) + 2 πn, θ = \frac{π}{2} + 2 πn

Show solutions in decimal form

θ = - 0.44291 \dots + 2 πn, θ = π + 0.44291 \dots + 2 πn, θ = \frac{π}{2} + 2 πn

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

csc (θ) = - \frac{2 3}{3}

2 sin (\frac{x}{3}) + 3 = 0

tan (θ) = \frac{15}{8}

sin (θ) = 4

What is the general solution for -7sin^2(θ)+4sin(θ)=-3 ?
The general solution for -7sin^2(θ)+4sin(θ)=-3 is θ=-0.44291…+2pin,θ=pi+0.44291…+2pin,θ= pi/2+2pin