What is the general solution for csc(θ)=-7/3 ?

The general solution for csc(θ)=-7/3 is θ=-0.44291…+2pin,θ=pi+0.44291…+2pin

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csc(θ)=-7/3

csc (θ) = - \frac{7}{3}

θ = - 0.44291 \dots + 2 πn, θ = π + 0.44291 \dots + 2 πn

Degrees

θ = - 25.37693 \dots^{\circ} + 36 0^{\circ} n, θ = 205.37693 \dots^{\circ} + 36 0^{\circ} n

Solution steps

csc (θ) = - \frac{7}{3}

Apply trig inverse properties

csc (θ) = - \frac{7}{3}

General solutions for

csc (θ) = - \frac{7}{3}

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

θ = arccsc (- \frac{7}{3}) + 2 πn, θ = π + arccsc (\frac{7}{3}) + 2 πn

θ = arccsc (- \frac{7}{3}) + 2 πn, θ = π + arccsc (\frac{7}{3}) + 2 πn

Show solutions in decimal form

θ = - 0.44291 \dots + 2 πn, θ = π + 0.44291 \dots + 2 πn

sin (θ) = \frac{5}{8}

arctan (2 x) + arctan (x) = \frac{π}{4}

tan (a) = 1

cos (2 θ) = 2, cos^{2} (θ) - 1 = 2, (- \frac{3}{5})^{2} - 1 = - \frac{7}{25}

2 sin (2 θ) = 1, 0 \leq θ \leq 2 π

What is the general solution for csc(θ)=-7/3 ?
The general solution for csc(θ)=-7/3 is θ=-0.44291…+2pin,θ=pi+0.44291…+2pin