What is the general solution for -20csc(x)=40 ?

The general solution for -20csc(x)=40 is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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-20csc(x)=40

- 20 csc (x) = 40

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

- 20 csc (x) = 40

Divide both sides by

- 20

- 20 csc (x) = 40

Divide both sides by

- 20

\frac{- 20 csc ( x )}{- 20} = \frac{40}{- 20}

Simplify

\frac{- 20 csc ( x )}{- 20} = \frac{40}{- 20}

Simplify

\frac{- 20 csc ( x )}{- 20} : csc (x)

\frac{- 20 csc ( x )}{- 20}

Apply the fraction rule:

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

= \frac{20 csc ( x )}{20}

Divide the numbers:

\frac{20}{20} = 1

= csc (x)

Simplify

\frac{40}{- 20} : - 2

\frac{40}{- 20}

Apply the fraction rule:

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

= - \frac{40}{20}

Divide the numbers:

\frac{40}{20} = 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

0 = 4 ∣ sin (6 θ) ∣

5 sin^{2} (θ) - 11 sin (θ) + 6 = 0

cos (x) = \frac{11}{14}, sin (x)

sin^{2} (2 x) + cos^{2} (3 x) = 1

sin (θ) = 0.9848

What is the general solution for -20csc(x)=40 ?
The general solution for -20csc(x)=40 is x=(7pi)/6+2pin,x=(11pi)/6+2pin