What is the general solution for csc(θ)= 4/3 ?

The general solution for csc(θ)= 4/3 is θ=0.84806…+2pin,θ=pi-0.84806…+2pin

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csc(θ)= 4/3

csc (θ) = \frac{4}{3}

θ = 0.84806 \dots + 2 πn, θ = π - 0.84806 \dots + 2 πn

Degrees

θ = 48.59037 \dots^{\circ} + 36 0^{\circ} n, θ = 131.40962 \dots^{\circ} + 36 0^{\circ} n

Solution steps

csc (θ) = \frac{4}{3}

Apply trig inverse properties

csc (θ) = \frac{4}{3}

General solutions for

csc (θ) = \frac{4}{3}

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

θ = arccsc (\frac{4}{3}) + 2 πn, θ = π - arccsc (\frac{4}{3}) + 2 πn

θ = arccsc (\frac{4}{3}) + 2 πn, θ = π - arccsc (\frac{4}{3}) + 2 πn

Show solutions in decimal form

θ = 0.84806 \dots + 2 πn, θ = π - 0.84806 \dots + 2 πn

9^{s i n (x) - 1} + 3 = 3^{s i n (x)} + 3^{s i n (x) - 1}

3 + 3 sin (θ) = 9 sin (θ)

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

5 sin (3 x) = - 2

cos^{2} (x) - 1 = 0, 0 \leq x < 2 π

What is the general solution for csc(θ)= 4/3 ?
The general solution for csc(θ)= 4/3 is θ=0.84806…+2pin,θ=pi-0.84806…+2pin