What is the general solution for 4csc(x)+8=0 ?

The general solution for 4csc(x)+8=0 is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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4csc(x)+8=0

4 csc (x) + 8 = 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

4 csc (x) + 8 = 0

Move

8

to the right side

4 csc (x) + 8 = 0

Subtract

8

from both sides

4 csc (x) + 8 - 8 = 0 - 8

Simplify

4 csc (x) = - 8

4 csc (x) = - 8

Divide both sides by

4

4 csc (x) = - 8

Divide both sides by

4

\frac{4 csc ( x )}{4} = \frac{- 8}{4}

Simplify

\frac{4 csc ( x )}{4} = \frac{- 8}{4}

Simplify

\frac{4 csc ( x )}{4} : csc (x)

\frac{4 csc ( x )}{4}

Divide the numbers:

\frac{4}{4} = 1

= csc (x)

Simplify

\frac{- 8}{4} : - 2

\frac{- 8}{4}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{8}{4}

Divide the numbers:

\frac{8}{4} = 2

= - 2

csc (x) = - 2

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

What is the general solution for 4csc(x)+8=0 ?
The general solution for 4csc(x)+8=0 is x=(7pi)/6+2pin,x=(11pi)/6+2pin