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

The general solution for 9*csc(x)=6sqrt(3),(-infinity ,infinity) is

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9*csc(x)=6sqrt(3),(-infinity ,infinity)

9 \cdot csc (x) = 63, (- \infty, \infty)

x = \frac{π}{3}, x = \frac{2 π}{3}, x = \frac{7 π}{3}, x = \frac{8 π}{3}, x = \frac{13 π}{3}, x = \frac{14 π}{3}, x = \frac{19 π}{3}, x = \frac{20 π}{3}, x = \frac{25 π}{3}, x = \frac{26 π}{3}, x = - \frac{5 π}{3}, x = - \frac{4 π}{3}, x = - \frac{11 π}{3}, x = - \frac{10 π}{3}, x = - \frac{17 π}{3}, x = - \frac{16 π}{3}, x = - \frac{23 π}{3}, x = - \frac{22 π}{3}

Degrees

x = 6 0^{\circ}, x = 12 0^{\circ}, x = 42 0^{\circ}, x = 48 0^{\circ}, x = 78 0^{\circ}, x = 84 0^{\circ}, x = 114 0^{\circ}, x = 120 0^{\circ}, x = 150 0^{\circ}, x = 156 0^{\circ}, x = - 30 0^{\circ}, x = - 24 0^{\circ}, x = - 66 0^{\circ}, x = - 60 0^{\circ}, x = - 102 0^{\circ}, x = - 96 0^{\circ}, x = - 138 0^{\circ}, x = - 132 0^{\circ}

Solution steps

9 csc (x) = 63, (- \infty, \infty)

Divide both sides by

9

9 csc (x) = 63

Divide both sides by

9

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

Simplify

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

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

General solutions for

csc (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

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

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

Solutions for the range

(- \infty, \infty)

x = \frac{π}{3}, x = \frac{2 π}{3}, x = \frac{7 π}{3}, x = \frac{8 π}{3}, x = \frac{13 π}{3}, x = \frac{14 π}{3}, x = \frac{19 π}{3}, x = \frac{20 π}{3}, x = \frac{25 π}{3}, x = \frac{26 π}{3}, x = - \frac{5 π}{3}, x = - \frac{4 π}{3}, x = - \frac{11 π}{3}, x = - \frac{10 π}{3}, x = - \frac{17 π}{3}, x = - \frac{16 π}{3}, x = - \frac{23 π}{3}, x = - \frac{22 π}{3}

cos (2 x - \frac{π}{2}) = 1

tan (x) = - 2

sin (θ) = \frac{1}{8}

5 sin (θ) + 1 = 0

sec (3 θ) = 2

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