What is the general solution for csc(x)=-1 ?

The general solution for csc(x)=-1 is x=(3pi)/2+2pin

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csc(x)=-1

csc (x) = - 1

x = \frac{3 π}{2} + 2 πn

Degrees

x = 27 0^{\circ} + 36 0^{\circ} n

Solution steps

csc (x) = - 1

General solutions for

csc (x) = - 1

csc (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

x = \frac{3 π}{2} + 2 πn

x = \frac{3 π}{2} + 2 πn

(2 sin^{2} (x) - 1) (tan^{2} (x) - 3) = 0

tan (x) = \frac{4}{3}

sec^{2} (x) = 2

sinh (3 x) - 3 sinh (x) = 0

cos (4 x) = sin (2 x)

What is the general solution for csc(x)=-1 ?
The general solution for csc(x)=-1 is x=(3pi)/2+2pin