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 = 233.13010 \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

2 - sec^{2} (x) = 0

4 sin (θ) - 22 = 0

sec (θ) = \frac{2}{3}

3 cos (2 θ) - 5 sin (θ) - 9 = - 5

tan (x) = 1, 0 \leq x \leq 2 π

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