What is the general solution for sin(θ)=-4/9 ?

The general solution for sin(θ)=-4/9 is θ=-0.46055…+2pin,θ=pi+0.46055…+2pin

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sin(θ)=-4/9

sin (θ) = - \frac{4}{9}

θ = - 0.46055 \dots + 2 πn, θ = π + 0.46055 \dots + 2 πn

Degrees

θ = - 26.38779 \dots^{\circ} + 36 0^{\circ} n, θ = 206.38779 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = - \frac{4}{9}

Apply trig inverse properties

sin (θ) = - \frac{4}{9}

General solutions for

sin (θ) = - \frac{4}{9}

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

θ = arcsin (- \frac{4}{9}) + 2 πn, θ = π + arcsin (\frac{4}{9}) + 2 πn

θ = arcsin (- \frac{4}{9}) + 2 πn, θ = π + arcsin (\frac{4}{9}) + 2 πn

Show solutions in decimal form

θ = - 0.46055 \dots + 2 πn, θ = π + 0.46055 \dots + 2 πn

- sin (y) = 0

0 = 2 + 4 sin (θ)

cos (x) = \frac{71}{81}

2 sin^{2} (2 x) - sin (2 x) - 3 = 0

cos (π + x) + cos (π + x) = 1

What is the general solution for sin(θ)=-4/9 ?
The general solution for sin(θ)=-4/9 is θ=-0.46055…+2pin,θ=pi+0.46055…+2pin