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

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

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csc(θ)=-3/2 ,pi<θ<(3pi)/2 ,sin(θ)

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

θ = π + 0.72972 \dots

Degrees

θ = 221.81031 \dots^{\circ}

Solution steps

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

Apply trig inverse properties

csc (θ) = - \frac{3}{2}

General solutions for

csc (θ) = - \frac{3}{2}

csc (x) = - a \Rightarrow x = arccsc (- a) + 2 πn, x = π + arccsc (a) + 2 πn

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

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

Solutions for the range

π < θ < \frac{3 π}{2}

θ = π + arccsc (\frac{3}{2})

Show solutions in decimal form

θ = π + 0.72972 \dots

\frac{2 - 3 sin ( θ )}{2} = - 3 sin (θ)

sin (2 x) = \frac{- 3}{2}

x, arctan (x) = \frac{π y}{4}

1 = 4 sin (x)

tan (x) = \frac{45}{67}

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