What is the general solution for sin(θ)=-4/5 ,(3pi)/2 <θ<2pi ?

The general solution for sin(θ)=-4/5 ,(3pi)/2 <θ<2pi is θ=-0.92729…+2pi

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sin(θ)=-4/5 ,(3pi)/2 <θ<2pi

sin (θ) = - \frac{4}{5}, \frac{3 π}{2} < θ < 2 π

θ = - 0.92729 \dots + 2 π

Degrees

θ = 306.86989 \dots^{\circ}

Solution steps

sin (θ) = - \frac{4}{5}, \frac{3 π}{2} < θ < 2 π

Apply trig inverse properties

sin (θ) = - \frac{4}{5}

General solutions for

sin (θ) = - \frac{4}{5}

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

θ = arcsin (- \frac{4}{5}) + 2 πn, θ = π + arcsin (\frac{4}{5}) + 2 πn

θ = arcsin (- \frac{4}{5}) + 2 πn, θ = π + arcsin (\frac{4}{5}) + 2 πn

Solutions for the range

\frac{3 π}{2} < θ < 2 π

θ = - arcsin (\frac{4}{5}) + 2 π

Show solutions in decimal form

θ = - 0.92729 \dots + 2 π

4 cos (x) + sin^{2} (x) = 3 cos^{2} (x) + 2

5 tan (B) + 13 = 0

tan^{2} (x) = 3 tan (x)

2 cos^{2} (x) - 2 = 0

sin (θ - \frac{π}{4}) - 1 = 0

What is the general solution for sin(θ)=-4/5 ,(3pi)/2 <θ<2pi ?
The general solution for sin(θ)=-4/5 ,(3pi)/2 <θ<2pi is θ=-0.92729…+2pi