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

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

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7sin^2(θ)-4sin(θ)=3

7 sin^{2} (θ) - 4 sin (θ) = 3

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

Solution steps

7 sin^{2} (θ) - 4 sin (θ) = 3

Solve by substitution

sin (θ) = 1, sin (θ) = - \frac{3}{7}

sin (θ) = 1 : θ = \frac{π}{2} + 2 πn

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

Combine all the solutions

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

Show solutions in decimal form

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

tan (θ) - cot (θ) = 0

csc^{3} (x) + csc^{2} (x) = \frac{4}{3} csc (x) + \frac{4}{3}

6 sec^{2} (x) tan (x) = 12 tan (x)

cos (θ) + cos (2 θ) = 0

sin (2 x) = 2

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