What is the general solution for sin(θ)= 2/9 ?

The general solution for sin(θ)= 2/9 is θ=0.22409…+2pin,θ=pi-0.22409…+2pin

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sin(θ)= 2/9

sin (θ) = \frac{2}{9}

θ = 0.22409 \dots + 2 πn, θ = π - 0.22409 \dots + 2 πn

Solution steps

sin (θ) = \frac{2}{9}

Apply trig inverse properties

θ = arcsin (\frac{2}{9}) + 2 πn, θ = π - arcsin (\frac{2}{9}) + 2 πn

Show solutions in decimal form

θ = 0.22409 \dots + 2 πn, θ = π - 0.22409 \dots + 2 πn

- 2 sin^{2} (θ) + 9 sin (θ) = 8 sin (θ) - 1

sin^{2} (x) - sin (x) - 1 = 0

2 sec (x) - 4 = 0

sin (2 x) cos (x) + cos (2 x) sin (x) = - \frac{1}{2}

6 tan (x) sin (x) = - 5 sin (x)

What is the general solution for sin(θ)= 2/9 ?
The general solution for sin(θ)= 2/9 is θ=0.22409…+2pin,θ=pi-0.22409…+2pin