What is the general solution for (sqrt(116))/(sin(90))= 4/(sin(x)) ?

The general solution for (sqrt(116))/(sin(90))= 4/(sin(x)) is x=0.38050…+360n,x=180-0.38050…+360n

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(sqrt(116))/(sin(90))= 4/(sin(x))

\frac{116}{sin ( 9 0 ^{\circ} )} = \frac{4}{sin ( x )}

x = 0.38050 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.38050 \dots + 36 0^{\circ} n

Solution steps

\frac{116}{sin ( 9 0 ^{\circ} )} = \frac{4}{sin ( x )}

sin (9 0^{\circ}) = 1

\frac{116}{1} = \frac{4}{sin ( x )}

Cross multiply

229 sin (x) = 4

Divide both sides by

229

sin (x) = \frac{2 29}{29}

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Combine undefined points with solutions:

sin (x) = \frac{2 29}{29}

Apply trig inverse properties

x = arcsin (\frac{2 29}{29}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{2 29}{29}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.38050 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.38050 \dots + 36 0^{\circ} n

\frac{3}{cos ^{2} ( x )} = \frac{7 + 4}{cot ( x )}

sin (x) = 0.01

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

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

sin (x) = \frac{4}{5}, \frac{π}{2} \leq 0 < π, sin (2 x)

What is the general solution for (sqrt(116))/(sin(90))= 4/(sin(x)) ?
The general solution for (sqrt(116))/(sin(90))= 4/(sin(x)) is x=0.38050…+360n,x=180-0.38050…+360n