What is the general solution for 6/(sin(60))= 4/(sin(x)) ?

The general solution for 6/(sin(60))= 4/(sin(x)) is x=0.61547…+360n,x=180-0.61547…+360n

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6/(sin(60))= 4/(sin(x))

\frac{6}{sin ( 6 0 ^{\circ} )} = \frac{4}{sin ( x )}

x = 0.61547 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.61547 \dots + 36 0^{\circ} n

Solution steps

\frac{6}{sin ( 6 0 ^{\circ} )} = \frac{4}{sin ( x )}

sin (6 0^{\circ}) = \frac{3}{2}

\frac{6}{\frac{3}{2}} = \frac{4}{sin ( x )}

Cross multiply

6 sin (x) = 23

Divide both sides by

6

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

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Combine undefined points with solutions:

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

Apply trig inverse properties

x = arcsin (\frac{3}{3}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{3}{3}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.61547 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.61547 \dots + 36 0^{\circ} n

10 = 14 + 8 sin (\frac{π t}{12})

sin (4 x) cos (x) - cos (4 x) sin (x) = 1

sec (θ) = \frac{10}{6}

x, 2 cos (3 x) = - 3

x, 7 - 3 cos (x) = 9 sin^{2} (x)

What is the general solution for 6/(sin(60))= 4/(sin(x)) ?
The general solution for 6/(sin(60))= 4/(sin(x)) is x=0.61547…+360n,x=180-0.61547…+360n