What is the general solution for csc(x)+2=0 ?

The general solution for csc(x)+2=0 is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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csc(x)+2=0

csc (x) + 2 = 0

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Degrees

x = 21 0^{\circ} + 36 0^{\circ} n, x = 33 0^{\circ} + 36 0^{\circ} n

Solution steps

csc (x) + 2 = 0

Move

2

to the right side

csc (x) + 2 = 0

Subtract

2

from both sides

csc (x) + 2 - 2 = 0 - 2

Simplify

csc (x) = - 2

csc (x) = - 2

General solutions for

csc (x) = - 2

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{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

tan (\frac{x}{2}) = 1

sin (\frac{x}{2}) = 0

sin (x) - 1 = cos (x)

cos (2 x) = - cos (x)

sin (x) = 3

What is the general solution for csc(x)+2=0 ?
The general solution for csc(x)+2=0 is x=(7pi)/6+2pin,x=(11pi)/6+2pin