What is the general solution for csc(θ)=-2 ?

The general solution for csc(θ)=-2 is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin

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csc(θ)=-2

csc (θ) = - 2

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

Degrees

θ = 21 0^{\circ} + 36 0^{\circ} n, θ = 33 0^{\circ} + 36 0^{\circ} n

Solution steps

csc (θ) = - 2

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

4 cos^{2} (x) - 1 = 0, 0 < x < 2 π

cos (\frac{2 x - π}{6}) = \frac{( 3 )}{2}, 0 < x < 2 π

4 sin (\frac{t}{2}) - 1 = 1

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

tan (θ) + cot (θ) = 4 sin (2 θ)

What is the general solution for csc(θ)=-2 ?
The general solution for csc(θ)=-2 is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin