What is the general solution for csc(θ)=-8/5 ?

The general solution for csc(θ)=-8/5 is θ=-0.67513…+2pin,θ=pi+0.67513…+2pin

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csc(θ)=-8/5

csc (θ) = - \frac{8}{5}

θ = - 0.67513 \dots + 2 πn, θ = π + 0.67513 \dots + 2 πn

Solution steps

csc (θ) = - \frac{8}{5}

Apply trig inverse properties

θ = arccsc (- \frac{8}{5}) + 2 πn, θ = π + arccsc (\frac{8}{5}) + 2 πn

Show solutions in decimal form

θ = - 0.67513 \dots + 2 πn, θ = π + 0.67513 \dots + 2 πn

cos^{2} (x) = 2 cos (x) + 3

3 sin (x) - cos (x) = 3

11 - sin (x) = cos (2 x)

sin^{3} (x) = sin (x), 0 \leq x \leq 2 π

x, 1 + cos (x) = 3 cos (x)

What is the general solution for csc(θ)=-8/5 ?
The general solution for csc(θ)=-8/5 is θ=-0.67513…+2pin,θ=pi+0.67513…+2pin