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}

Solution steps

csc (θ) = - 2, 0 \leq θ < 4 π

General solutions for

csc (θ) = - 2

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}

- sin^{2} (x) + cos^{2} (x) = sin (x) + 1

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

tan (x) + cot (x) = 5

5 sin^{2} (θ) + 12 sin (θ) + 7 = 0

3 sin (x) + 2 sin^{2} (x) = - 1

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