What is the general solution for csc(θ)=-3/2 ?

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

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csc(θ)=-3/2

csc (θ) = - \frac{3}{2}

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

Degrees

θ = - 41.81031 \dots^{\circ} + 36 0^{\circ} n, θ = 221.81031 \dots^{\circ} + 36 0^{\circ} n

Solution steps

csc (θ) = - \frac{3}{2}

Apply trig inverse properties

csc (θ) = - \frac{3}{2}

General solutions for

csc (θ) = - \frac{3}{2}

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

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

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

Show solutions in decimal form

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

4 cos (θ) = 0

\frac{sin ( 16 0 ^{\circ} )}{5} = \frac{sin ( c )}{4}

sin (x) + 2 = 0

sin (θ) = - \frac{24}{25}

cos (2 x) + 7 sin (x) - 4 = 0

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