What is the general solution for 2csc(x)+4=0 ?

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

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2csc(x)+4=0

2 csc (x) + 4 = 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

2 csc (x) + 4 = 0

Move

4

to the right side

2 csc (x) + 4 = 0

Subtract

4

from both sides

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

Simplify

2 csc (x) = - 4

2 csc (x) = - 4

Divide both sides by

2

2 csc (x) = - 4

Divide both sides by

2

\frac{2 csc ( x )}{2} = \frac{- 4}{2}

Simplify

\frac{2 csc ( x )}{2} = \frac{- 4}{2}

Simplify

\frac{2 csc ( x )}{2} : csc (x)

\frac{2 csc ( x )}{2}

Divide the numbers:

\frac{2}{2} = 1

= csc (x)

Simplify

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

\frac{- 4}{2}

Apply the fraction rule:

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

= - \frac{4}{2}

Divide the numbers:

\frac{4}{2} = 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

2 sin (x) = 3, 0 \leq x \leq 2 π

x, z = arcsin (x + y)

150 cos (x - 8) = 0

8 sin^{2} (x) - 6 sin (x) + 1 = 0

sin (5 x) - cos (3 0^{\circ}) = 0

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