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

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

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csc(θ)= 3/2 , pi/2 <θ<(3pi)/2

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

θ = π - 0.72972 \dots

Degrees

θ = 138.18968 \dots^{\circ}

Solution steps

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

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

\frac{π}{2} < θ < \frac{3 π}{2}

θ = π - arccsc (\frac{3}{2})

Show solutions in decimal form

θ = π - 0.72972 \dots

tan (x) = \frac{5.1}{4.2}

tan (3 x) \cdot tan (3 0^{\circ}) = 1

3 - 6 sin (2 x) = 0

\frac{1}{1} + cot^{2} (x) = sin^{2} (x)

x, 2 cos (x) = 2 cos (3 x)

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