What is the general solution for sin(θ)=-1/3 ,(3pi)/2 <θ<2pi ?

The general solution for sin(θ)=-1/3 ,(3pi)/2 <θ<2pi is θ=-0.33983…+2pi

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sin(θ)=-1/3 ,(3pi)/2 <θ<2pi

sin (θ) = - \frac{1}{3}, \frac{3 π}{2} < θ < 2 π

θ = - 0.33983 \dots + 2 π

Degrees

θ = 340.52877 \dots^{\circ}

Solution steps

sin (θ) = - \frac{1}{3}, \frac{3 π}{2} < θ < 2 π

Apply trig inverse properties

sin (θ) = - \frac{1}{3}

General solutions for

sin (θ) = - \frac{1}{3}

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

θ = arcsin (- \frac{1}{3}) + 2 πn, θ = π + arcsin (\frac{1}{3}) + 2 πn

θ = arcsin (- \frac{1}{3}) + 2 πn, θ = π + arcsin (\frac{1}{3}) + 2 πn

Solutions for the range

\frac{3 π}{2} < θ < 2 π

θ = - arcsin (\frac{1}{3}) + 2 π

Show solutions in decimal form

θ = - 0.33983 \dots + 2 π

4 cos (x) = 5 - 1

2 sin^{2} (θ) - 2 sin (θ) = 0

2 - cos (θ) = 2 + sin (θ)

sin (x) = 6757

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

What is the general solution for sin(θ)=-1/3 ,(3pi)/2 <θ<2pi ?
The general solution for sin(θ)=-1/3 ,(3pi)/2 <θ<2pi is θ=-0.33983…+2pi