What is the general solution for csc(θ)=4 ?

The general solution for csc(θ)=4 is θ=0.25268…+2pin,θ=pi-0.25268…+2pin

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csc(θ)=4

csc (θ) = 4

θ = 0.25268 \dots + 2 πn, θ = π - 0.25268 \dots + 2 πn

Solution steps

csc (θ) = 4

Apply trig inverse properties

θ = arccsc (4) + 2 πn, θ = π - arccsc (4) + 2 πn

Show solutions in decimal form

θ = 0.25268 \dots + 2 πn, θ = π - 0.25268 \dots + 2 πn

2 sin (2 θ) = - 2

2 sin (2 x) = 2

2 sec (θ) + 1 = 0

3 arccos (2 x) = 2 π

3 cos (x) = 1

What is the general solution for csc(θ)=4 ?
The general solution for csc(θ)=4 is θ=0.25268…+2pin,θ=pi-0.25268…+2pin