What is the general solution for csc(θ)=sqrt(5) ?

The general solution for csc(θ)=sqrt(5) is θ=0.46364…+2pin,θ=pi-0.46364…+2pin

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csc(θ)=sqrt(5)

csc (θ) = 5

θ = 0.46364 \dots + 2 πn, θ = π - 0.46364 \dots + 2 πn

Degrees

θ = 26.56505 \dots^{\circ} + 36 0^{\circ} n, θ = 153.43494 \dots^{\circ} + 36 0^{\circ} n

Solution steps

csc (θ) = 5

Apply trig inverse properties

csc (θ) = 5

General solutions for

csc (θ) = 5

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

θ = arccsc (5) + 2 πn, θ = π - arccsc (5) + 2 πn

θ = arccsc (5) + 2 πn, θ = π - arccsc (5) + 2 πn

Show solutions in decimal form

θ = 0.46364 \dots + 2 πn, θ = π - 0.46364 \dots + 2 πn

cot^{2} (x) = tan (\frac{x}{2})

cos (x) = \frac{15}{21}

2 cos (x) - cos^{2} (x) - sin^{2} (x) = 0

2 cos (x) - 1 = 0, 0 \leq x < 2 π

cos (t) = \frac{3}{5}

What is the general solution for csc(θ)=sqrt(5) ?
The general solution for csc(θ)=sqrt(5) is θ=0.46364…+2pin,θ=pi-0.46364…+2pin