What is the general solution for 7sin^2(θ)-5sin(θ)=2 ?

The general solution for 7sin^2(θ)-5sin(θ)=2 is θ= pi/2+2pin,θ=-0.28975…+2pin,θ=pi+0.28975…+2pin

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7sin^2(θ)-5sin(θ)=2

7 sin^{2} (θ) - 5 sin (θ) = 2

θ = \frac{π}{2} + 2 πn, θ = - 0.28975 \dots + 2 πn, θ = π + 0.28975 \dots + 2 πn

Solution steps

7 sin^{2} (θ) - 5 sin (θ) = 2

Solve by substitution

sin (θ) = 1, sin (θ) = - \frac{2}{7}

sin (θ) = 1 : θ = \frac{π}{2} + 2 πn

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

Combine all the solutions

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

Show solutions in decimal form

θ = \frac{π}{2} + 2 πn, θ = - 0.28975 \dots + 2 πn, θ = π + 0.28975 \dots + 2 πn

sec (2 x) = - (\frac{2}{3})

\frac{e ^{- l n (- \frac{s i n ( θ )}{c o s ( θ )})}}{2} \cdot sin (θ) = 0

7 sin (2 x) + 12 sin (x) = 0

x, cos (x) = cos (2 x)

cos (x) = 0.50074242

What is the general solution for 7sin^2(θ)-5sin(θ)=2 ?
The general solution for 7sin^2(θ)-5sin(θ)=2 is θ= pi/2+2pin,θ=-0.28975…+2pin,θ=pi+0.28975…+2pin