What is the general solution for csc(θ)=-5 ?

The general solution for csc(θ)=-5 is θ=-0.20135…+2pin,θ=pi+0.20135…+2pin

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csc(θ)=-5

csc (θ) = - 5

θ = - 0.20135 \dots + 2 πn, θ = π + 0.20135 \dots + 2 πn

Solution steps

csc (θ) = - 5

Apply trig inverse properties

θ = arccsc (- 5) + 2 πn, θ = π + arccsc (5) + 2 πn

Show solutions in decimal form

θ = - 0.20135 \dots + 2 πn, θ = π + 0.20135 \dots + 2 πn

- 50 \cdot cos (x) - 86.6025400000000 \dots \cdot sin (x) = 50

3 cos (2 θ) + sin (θ) - 3 = - 2

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

2 sin (2 x) + 5 = 4

x, sin (x) = cos (x)

What is the general solution for csc(θ)=-5 ?
The general solution for csc(θ)=-5 is θ=-0.20135…+2pin,θ=pi+0.20135…+2pin