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

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

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-2=csc(θ)

- 2 = csc (θ)

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

- 2 = csc (θ)

Switch sides

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

2 cot (x) = csc^{2} (x)

2 csc (2 x) cot (2 x) = 0

3 cos (y) + cot (y) = 0

2 sin (x) - 3 sin (x) + 1 = 0

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

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