What is the general solution for 3csc(θ)=4.5 ?

The general solution for 3csc(θ)=4.5 is θ=0.72972…+2pin,θ=pi-0.72972…+2pin

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3csc(θ)=4.5

3 csc (θ) = 4.5

θ = 0.72972 \dots + 2 πn, θ = π - 0.72972 \dots + 2 πn

Degrees

θ = 41.81031 \dots^{\circ} + 36 0^{\circ} n, θ = 138.18968 \dots^{\circ} + 36 0^{\circ} n

Solution steps

3 csc (θ) = 4.5

Divide both sides by

3

3 csc (θ) = 4.5

Divide both sides by

3

\frac{3 csc ( θ )}{3} = \frac{4.5}{3}

Simplify

csc (θ) = 1.5

csc (θ) = 1.5

Apply trig inverse properties

csc (θ) = 1.5

General solutions for

csc (θ) = 1.5

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

θ = arccsc (1.5) + 2 πn, θ = π - arccsc (1.5) + 2 πn

θ = arccsc (1.5) + 2 πn, θ = π - arccsc (1.5) + 2 πn

Show solutions in decimal form

θ = 0.72972 \dots + 2 πn, θ = π - 0.72972 \dots + 2 πn

cos^{3} (x) = \frac{1}{4 ( 3 cos ( x ) + cos ( 3 x ) )}

w, s (t) = A e^{- c t} cos (wt + θ)

2 = 2 sin (x)

6 sin (\frac{π}{4} x) = 3

sec (x) = 3, \frac{3 π}{2} \leq x \leq 2 π, sin (2 x)

What is the general solution for 3csc(θ)=4.5 ?
The general solution for 3csc(θ)=4.5 is θ=0.72972…+2pin,θ=pi-0.72972…+2pin