What is the general solution for csc(θ)= 5/4 ?

The general solution for csc(θ)= 5/4 is θ=0.92729…+2pin,θ=pi-0.92729…+2pin

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csc(θ)= 5/4

csc (θ) = \frac{5}{4}

θ = 0.92729 \dots + 2 πn, θ = π - 0.92729 \dots + 2 πn

Degrees

θ = 53.13010 \dots^{\circ} + 36 0^{\circ} n, θ = 126.86989 \dots^{\circ} + 36 0^{\circ} n

Solution steps

csc (θ) = \frac{5}{4}

Apply trig inverse properties

csc (θ) = \frac{5}{4}

General solutions for

csc (θ) = \frac{5}{4}

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

θ = arccsc (\frac{5}{4}) + 2 πn, θ = π - arccsc (\frac{5}{4}) + 2 πn

θ = arccsc (\frac{5}{4}) + 2 πn, θ = π - arccsc (\frac{5}{4}) + 2 πn

Show solutions in decimal form

θ = 0.92729 \dots + 2 πn, θ = π - 0.92729 \dots + 2 πn

8 sin^{3} (x) - 4 sin^{2} (x) - 6 sin (x) + 3 = 0

2 cos (x) = 1 - sin (x)

tan (2 θ) + tan (2 θ) = tan (4 θ)

1 - 7 cos (θ) = 8

tanh (x) = \frac{12}{13}

What is the general solution for csc(θ)= 5/4 ?
The general solution for csc(θ)= 5/4 is θ=0.92729…+2pin,θ=pi-0.92729…+2pin