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

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

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9csc(x)=6sqrt(3)

9 csc (x) = 63

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

Degrees

x = 6 0^{\circ} + 36 0^{\circ} n, x = 12 0^{\circ} + 36 0^{\circ} n

Solution steps

9 csc (x) = 63

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

5 sec (θ) - 2 sec^{2} (θ) = tan^{2} (θ) - 1

cos (2 x) + cos (x) = 0, (0, 2 π)

3 \cdot sin (\frac{x}{2}) + cos (x) = 1

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

3 sin (x) + 2 cos (x) = 1

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