What is the general solution for csc(θ)=-5/3 ?

The general solution for csc(θ)=-5/3 is θ=-0.64350…+2pin,θ=pi+0.64350…+2pin

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csc(θ)=-5/3

csc (θ) = - \frac{5}{3}

θ = - 0.64350 \dots + 2 πn, θ = π + 0.64350 \dots + 2 πn

Degrees

θ = - 36.86989 \dots^{\circ} + 36 0^{\circ} n, θ = 216.86989 \dots^{\circ} + 36 0^{\circ} n

Solution steps

csc (θ) = - \frac{5}{3}

Apply trig inverse properties

csc (θ) = - \frac{5}{3}

General solutions for

csc (θ) = - \frac{5}{3}

csc (x) = - a \Rightarrow x = arccsc (- a) + 2 πn, x = π + arccsc (a) + 2 πn

θ = arccsc (- \frac{5}{3}) + 2 πn, θ = π + arccsc (\frac{5}{3}) + 2 πn

θ = arccsc (- \frac{5}{3}) + 2 πn, θ = π + arccsc (\frac{5}{3}) + 2 πn

Show solutions in decimal form

θ = - 0.64350 \dots + 2 πn, θ = π + 0.64350 \dots + 2 πn

2 sin^{2} (t) cos (t) = 0

2 cos (θ) + sin (θ) = 0

2 sin^{2} (x) + sin (x) - 1 = 0, 0 < x < 2 π

5 sin (x) - 12 cos (x) = 13

sec (x) = 1.562641

What is the general solution for csc(θ)=-5/3 ?
The general solution for csc(θ)=-5/3 is θ=-0.64350…+2pin,θ=pi+0.64350…+2pin