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

The general solution for 7sin^2(θ)-3sin(θ)=4 is θ= pi/2+2pin,θ=-0.60824…+2pin,θ=pi+0.60824…+2pin

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7sin^2(θ)-3sin(θ)=4

7 sin^{2} (θ) - 3 sin (θ) = 4

θ = \frac{π}{2} + 2 πn, θ = - 0.60824 \dots + 2 πn, θ = π + 0.60824 \dots + 2 πn

Solution steps

7 sin^{2} (θ) - 3 sin (θ) = 4

Solve by substitution

sin (θ) = 1, sin (θ) = - \frac{4}{7}

sin (θ) = 1 : θ = \frac{π}{2} + 2 πn

sin (θ) = - \frac{4}{7} : θ = arcsin (- \frac{4}{7}) + 2 πn, θ = π + arcsin (\frac{4}{7}) + 2 πn

Combine all the solutions

θ = \frac{π}{2} + 2 πn, θ = arcsin (- \frac{4}{7}) + 2 πn, θ = π + arcsin (\frac{4}{7}) + 2 πn

Show solutions in decimal form

θ = \frac{π}{2} + 2 πn, θ = - 0.60824 \dots + 2 πn, θ = π + 0.60824 \dots + 2 πn

- 5 - 4 tan (θ) = - 1

sin (θ) = - \frac{7}{10}

10 cos (2 x) - 3 = 2

sin^{2} (θ) = 9 (cos (- θ) + 1)

sin (30 x) = 202.07

What is the general solution for 7sin^2(θ)-3sin(θ)=4 ?
The general solution for 7sin^2(θ)-3sin(θ)=4 is θ= pi/2+2pin,θ=-0.60824…+2pin,θ=pi+0.60824…+2pin