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

The general solution for csc(θ)=-3 is θ=-0.33983…+2pin,θ=pi+0.33983…+2pin

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csc(θ)=-3

csc (θ) = - 3

θ = - 0.33983 \dots + 2 πn, θ = π + 0.33983 \dots + 2 πn

Degrees

θ = - 19.47122 \dots^{\circ} + 36 0^{\circ} n, θ = 199.47122 \dots^{\circ} + 36 0^{\circ} n

Solution steps

csc (θ) = - 3

Apply trig inverse properties

csc (θ) = - 3

General solutions for

csc (θ) = - 3

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

θ = arccsc (- 3) + 2 πn, θ = π + arccsc (3) + 2 πn

θ = arccsc (- 3) + 2 πn, θ = π + arccsc (3) + 2 πn

Show solutions in decimal form

θ = - 0.33983 \dots + 2 πn, θ = π + 0.33983 \dots + 2 πn

4 cos (x) - 2 = 2 tan (x) cot (x) - sec (x)

11 (1 - cos (θ)) = sin^{2} (θ)

cos^{2} (x) - \frac{1}{2} = 0, 0 \leq x \leq 2 π

x, tan (x) = tan (y)

4 cos (θ) + 3 = 0

What is the general solution for csc(θ)=-3 ?
The general solution for csc(θ)=-3 is θ=-0.33983…+2pin,θ=pi+0.33983…+2pin