What is the general solution for csc(θ)=-2,0<= θ<4pi ?

The general solution for csc(θ)=-2,0<= θ<4pi is θ=(7pi)/6 ,θ=(11pi)/6 ,θ=(19pi)/6 ,θ=(23pi)/6

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csc(θ)=-2,0<= θ<4pi

csc (θ) = - 2, 0 \leq θ < 4 π

θ = \frac{7 π}{6}, θ = \frac{11 π}{6}, θ = \frac{19 π}{6}, θ = \frac{23 π}{6}

Degrees

θ = 21 0^{\circ}, θ = 33 0^{\circ}, θ = 57 0^{\circ}, θ = 69 0^{\circ}

Solution steps

csc (θ) = - 2, 0 \leq θ < 4 π

General solutions for

csc (θ) = - 2

csc (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Solutions for the range

0 \leq θ < 4 π

θ = \frac{7 π}{6}, θ = \frac{11 π}{6}, θ = \frac{19 π}{6}, θ = \frac{23 π}{6}

What is the general solution for csc(θ)=-2,0<= θ<4pi ?
The general solution for csc(θ)=-2,0<= θ<4pi is θ=(7pi)/6 ,θ=(11pi)/6 ,θ=(19pi)/6 ,θ=(23pi)/6