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

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

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csc(x)=-3/2

csc (x) = - \frac{3}{2}

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

Degrees

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

Solution steps

csc (x) = - \frac{3}{2}

Apply trig inverse properties

csc (x) = - \frac{3}{2}

General solutions for

csc (x) = - \frac{3}{2}

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

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

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

Show solutions in decimal form

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

1 + 3 sin (θ) = 0

\frac{tan ( 2 x )}{sin ( x )} = - 2

sin (A) = 0.5

cos (θ) = tan (θ)

tan (\frac{π}{4} + x) = \frac{1 - tan ( x )}{1 + tan ( x )}

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