What is the general solution for csc(θ)=-37/12 ,(3pi)/2 <= θ<= 2pi ?

The general solution for csc(θ)=-37/12 ,(3pi)/2 <= θ<= 2pi is θ=-0.33029…+2pi

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csc(θ)=-37/12 ,(3pi)/2 <= θ<= 2pi

csc (θ) = - \frac{37}{12}, \frac{3 π}{2} \leq θ \leq 2 π

θ = - 0.33029 \dots + 2 π

Degrees

θ = 341.07535 \dots^{\circ}

Solution steps

csc (θ) = - \frac{37}{12}, \frac{3 π}{2} \leq θ \leq 2 π

Apply trig inverse properties

csc (θ) = - \frac{37}{12}

General solutions for

csc (θ) = - \frac{37}{12}

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

θ = arccsc (- \frac{37}{12}) + 2 πn, θ = π + arccsc (\frac{37}{12}) + 2 πn

θ = arccsc (- \frac{37}{12}) + 2 πn, θ = π + arccsc (\frac{37}{12}) + 2 πn

Solutions for the range

\frac{3 π}{2} \leq θ \leq 2 π

θ = - arccsc (\frac{37}{12}) + 2 π

Show solutions in decimal form

θ = - 0.33029 \dots + 2 π

\frac{3}{2} = 2 \cdot 25 sin (\frac{θ}{2})

sin^{2} (x) - sin (x) - 12 = 0

7 sin (2 ϕ) + 12 cos (ϕ) = 0

sec (\frac{θ}{2}) = cos (\frac{θ}{2})

2 cos^{2} (x) - 1.28 = 0

What is the general solution for csc(θ)=-37/12 ,(3pi)/2 <= θ<= 2pi ?
The general solution for csc(θ)=-37/12 ,(3pi)/2 <= θ<= 2pi is θ=-0.33029…+2pi