What is the general solution for sin(θ)=(-2)/3 ?

The general solution for sin(θ)=(-2)/3 is θ=-0.72972…+2pin,θ=pi+0.72972…+2pin

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sin(θ)=(-2)/3

sin (θ) = \frac{- 2}{3}

θ = - 0.72972 \dots + 2 πn, θ = π + 0.72972 \dots + 2 πn

Degrees

θ = - 41.81031 \dots^{\circ} + 36 0^{\circ} n, θ = 221.81031 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = \frac{- 2}{3}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

sin (θ) = - \frac{2}{3}

Apply trig inverse properties

sin (θ) = - \frac{2}{3}

General solutions for

sin (θ) = - \frac{2}{3}

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

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

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

Show solutions in decimal form

θ = - 0.72972 \dots + 2 πn, θ = π + 0.72972 \dots + 2 πn

sec^{2} (θ) + csc^{2} (θ) = 4

cos (\frac{θ}{3}) = sin (θ)

sin (x) - cos (x) = \frac{1}{5}

tan (θ) = \frac{- 2}{3}

cos (θ) tan^{2} (θ) = 3 cos (θ)

What is the general solution for sin(θ)=(-2)/3 ?
The general solution for sin(θ)=(-2)/3 is θ=-0.72972…+2pin,θ=pi+0.72972…+2pin