What is the general solution for (13)/(sin(108))= 9/(sin(x)) ?

The general solution for (13)/(sin(108))= 9/(sin(x)) is x=0.71872…+360n,x=180-0.71872…+360n

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(13)/(sin(108))= 9/(sin(x))

\frac{13}{sin ( 10 8 ^{\circ} )} = \frac{9}{sin ( x )}

x = 0.71872 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.71872 \dots + 36 0^{\circ} n

Solution steps

\frac{13}{sin ( 10 8 ^{\circ} )} = \frac{9}{sin ( x )}

sin (10 8^{\circ}) = \frac{2 5 + 5}{4}

\frac{13}{\frac{2 5 + 5}{4}} = \frac{9}{sin ( x )}

Cross multiply

13 sin (x) = \frac{9 2 5 + 5}{4}

Divide both sides by

13

sin (x) = \frac{9 2 5 + 5}{52}

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Combine undefined points with solutions:

sin (x) = \frac{9 2 5 + 5}{52}

Apply trig inverse properties

x = arcsin (\frac{9 2 5 + 5}{52}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{9 2 5 + 5}{52}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.71872 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.71872 \dots + 36 0^{\circ} n

tan^{2} (x) + 5 cos (x) - 8 = 0

3 sin (x) = 2 - 2 sin^{2} (x)

100 = 100 + 40 sin (\frac{9 π}{4} t)

tan (φ) = - \frac{1}{3}

sin (3 m) = 0

What is the general solution for (13)/(sin(108))= 9/(sin(x)) ?
The general solution for (13)/(sin(108))= 9/(sin(x)) is x=0.71872…+360n,x=180-0.71872…+360n