What is the general solution for sin(θ)=-8/9 ?

The general solution for sin(θ)=-8/9 is θ=-1.09491…+2pin,θ=pi+1.09491…+2pin

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sin(θ)=-8/9

sin (θ) = - \frac{8}{9}

θ = - 1.09491 \dots + 2 πn, θ = π + 1.09491 \dots + 2 πn

Degrees

θ = - 62.73395 \dots^{\circ} + 36 0^{\circ} n, θ = 242.73395 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = - \frac{8}{9}

Apply trig inverse properties

sin (θ) = - \frac{8}{9}

General solutions for

sin (θ) = - \frac{8}{9}

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

θ = arcsin (- \frac{8}{9}) + 2 πn, θ = π + arcsin (\frac{8}{9}) + 2 πn

θ = arcsin (- \frac{8}{9}) + 2 πn, θ = π + arcsin (\frac{8}{9}) + 2 πn

Show solutions in decimal form

θ = - 1.09491 \dots + 2 πn, θ = π + 1.09491 \dots + 2 πn

2 sin^{2} (x) + 5 sin (x) - 12 = 0

3 tan (x - \frac{π}{5}) - 1 = 0

x, 0 = 4 - \frac{1}{cos ^{2} ( x )}

tan (θ) = \frac{17}{12}

csc^{2} (θ) = 2 cot (θ)

What is the general solution for sin(θ)=-8/9 ?
The general solution for sin(θ)=-8/9 is θ=-1.09491…+2pin,θ=pi+1.09491…+2pin