What is the general solution for -6sqrt(3)=-9csc(3x) ?

The general solution for -6sqrt(3)=-9csc(3x) is x= pi/9+(2pin)/3 ,x=(2pi)/9+(2pin)/3

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Popular >

-6sqrt(3)=-9csc(3x)

Solution

- 63 = - 9 csc (3 x)

Solution

x = \frac{π}{9} + \frac{2 πn}{3}, x = \frac{2 π}{9} + \frac{2 πn}{3}

Degrees

x = 2 0^{\circ} + 12 0^{\circ} n, x = 4 0^{\circ} + 12 0^{\circ} n

Solution steps

- 63 = - 9 csc (3 x)

Switch sides

- 9 csc (3 x) = - 63

Divide both sides by

- 9

- 9 csc (3 x) = - 63

Divide both sides by

- 9

\frac{- 9 csc ( 3 x )}{- 9} = \frac{- 6 3}{- 9}

Simplify

\frac{- 9 csc ( 3 x )}{- 9} = \frac{- 6 3}{- 9}

Simplify

\frac{- 9 csc ( 3 x )}{- 9} : csc (3 x)

\frac{- 9 csc ( 3 x )}{- 9}

Apply the fraction rule:

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

= \frac{9 csc ( 3 x )}{9}

Divide the numbers:

\frac{9}{9} = 1

= csc (3 x)

Simplify

\frac{- 6 3}{- 9} : \frac{2 3}{3}

\frac{- 6 3}{- 9}

Apply the fraction rule:

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

= \frac{6 3}{9}

Cancel the common factor:

3

= \frac{2 3}{3}

csc (3 x) = \frac{2 3}{3}

csc (3 x) = \frac{2 3}{3}

csc (3 x) = \frac{2 3}{3}

General solutions for

csc (3 x) = \frac{2 3}{3}

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

3 x = \frac{π}{3} + 2 πn, 3 x = \frac{2 π}{3} + 2 πn

3 x = \frac{π}{3} + 2 πn, 3 x = \frac{2 π}{3} + 2 πn

Solve

3 x = \frac{π}{3} + 2 πn : x = \frac{π}{9} + \frac{2 πn}{3}

3 x = \frac{π}{3} + 2 πn

Divide both sides by

3

3 x = \frac{π}{3} + 2 πn

Divide both sides by

3

\frac{3 x}{3} = \frac{\frac{π}{3}}{3} + \frac{2 πn}{3}

Simplify

\frac{3 x}{3} = \frac{\frac{π}{3}}{3} + \frac{2 πn}{3}

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

\frac{\frac{π}{3}}{3} + \frac{2 πn}{3} : \frac{π}{9} + \frac{2 πn}{3}

\frac{\frac{π}{3}}{3} + \frac{2 πn}{3}

\frac{\frac{π}{3}}{3} = \frac{π}{9}

\frac{\frac{π}{3}}{3}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{3 \cdot 3}

Multiply the numbers:

3 \cdot 3 = 9

= \frac{π}{9}

= \frac{π}{9} + \frac{2 πn}{3}

x = \frac{π}{9} + \frac{2 πn}{3}

x = \frac{π}{9} + \frac{2 πn}{3}

x = \frac{π}{9} + \frac{2 πn}{3}

Solve

3 x = \frac{2 π}{3} + 2 πn : x = \frac{2 π}{9} + \frac{2 πn}{3}

3 x = \frac{2 π}{3} + 2 πn

Divide both sides by

3

3 x = \frac{2 π}{3} + 2 πn

Divide both sides by

3

\frac{3 x}{3} = \frac{\frac{2 π}{3}}{3} + \frac{2 πn}{3}

Simplify

\frac{3 x}{3} = \frac{\frac{2 π}{3}}{3} + \frac{2 πn}{3}

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

\frac{\frac{2 π}{3}}{3} + \frac{2 πn}{3} : \frac{2 π}{9} + \frac{2 πn}{3}

\frac{\frac{2 π}{3}}{3} + \frac{2 πn}{3}

\frac{\frac{2 π}{3}}{3} = \frac{2 π}{9}

\frac{\frac{2 π}{3}}{3}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{2 π}{3 \cdot 3}

Multiply the numbers:

3 \cdot 3 = 9

= \frac{2 π}{9}

= \frac{2 π}{9} + \frac{2 πn}{3}

x = \frac{2 π}{9} + \frac{2 πn}{3}

x = \frac{2 π}{9} + \frac{2 πn}{3}

x = \frac{2 π}{9} + \frac{2 πn}{3}

x = \frac{π}{9} + \frac{2 πn}{3}, x = \frac{2 π}{9} + \frac{2 πn}{3}

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1 + sin (θ) = 1 + cos (θ)

tan(x)=tan(40)tan(50)

tan (x) = tan (4 0^{\circ}) tan (5 0^{\circ})

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cos(x)=(7.2)/(9.4)

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Frequently Asked Questions (FAQ)

What is the general solution for -6sqrt(3)=-9csc(3x) ?
The general solution for -6sqrt(3)=-9csc(3x) is x= pi/9+(2pin)/3 ,x=(2pi)/9+(2pin)/3