What is the general solution for 4csc(θ)-5=0 ?

The general solution for 4csc(θ)-5=0 is θ=0.92729…+2pin,θ=pi-0.92729…+2pin

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4csc(θ)-5=0

4 csc (θ) - 5 = 0

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

Solution steps

4 csc (θ) - 5 = 0

Move

5

to the right side

4 csc (θ) = 5

Divide both sides by

4

csc (θ) = \frac{5}{4}

Apply trig inverse properties

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

tan (4 x) + 3 = 0

2 sin (x) + 4 = 5

x, z = y sin (4 x)

csc (x) cot (x) = 0

\frac{1}{csc ^{2} ( a )} = 1 - sin^{2} (a)

What is the general solution for 4csc(θ)-5=0 ?
The general solution for 4csc(θ)-5=0 is θ=0.92729…+2pin,θ=pi-0.92729…+2pin