What is the general solution for csc(θ)=-1.343 ?

The general solution for csc(θ)=-1.343 is θ=-0.83993…+2pin,θ=pi+0.83993…+2pin

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csc(θ)=-1.343

csc (θ) = - 1.343

θ = - 0.83993 \dots + 2 πn, θ = π + 0.83993 \dots + 2 πn

Degrees

θ = - 48.12489 \dots^{\circ} + 36 0^{\circ} n, θ = 228.12489 \dots^{\circ} + 36 0^{\circ} n

Solution steps

csc (θ) = - 1.343

Apply trig inverse properties

csc (θ) = - 1.343

General solutions for

csc (θ) = - 1.343

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

θ = arccsc (- 1.343) + 2 πn, θ = π + arccsc (1.343) + 2 πn

θ = arccsc (- 1.343) + 2 πn, θ = π + arccsc (1.343) + 2 πn

Show solutions in decimal form

θ = - 0.83993 \dots + 2 πn, θ = π + 0.83993 \dots + 2 πn

csc (θ) = - \frac{3}{2}, π < θ < \frac{3 π}{2}, sin (θ)

\frac{2 - 3 sin ( θ )}{2} = - 3 sin (θ)

sin (2 x) = \frac{- 3}{2}

x, arctan (x) = \frac{π y}{4}

1 = 4 sin (x)

What is the general solution for csc(θ)=-1.343 ?
The general solution for csc(θ)=-1.343 is θ=-0.83993…+2pin,θ=pi+0.83993…+2pin