What is the general solution for (30)/(sin(x))=(50)/(sin(90)) ?

The general solution for (30)/(sin(x))=(50)/(sin(90)) is x=0.64350…+360n,x=180-0.64350…+360n

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(30)/(sin(x))=(50)/(sin(90))

\frac{30}{sin ( x )} = \frac{50}{sin ( 9 0 ^{\circ} )}

x = 0.64350 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.64350 \dots + 36 0^{\circ} n

Solution steps

\frac{30}{sin ( x )} = \frac{50}{sin ( 9 0 ^{\circ} )}

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

\frac{30}{sin ( x )} = \frac{50}{1}

Cross multiply

30 = sin (x) \cdot 50

Switch sides

sin (x) \cdot 50 = 30

Divide both sides by

50

sin (x) = \frac{3}{5}

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Combine undefined points with solutions:

sin (x) = \frac{3}{5}

Apply trig inverse properties

x = arcsin (\frac{3}{5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{3}{5}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.64350 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.64350 \dots + 36 0^{\circ} n

cos (θ) = \frac{2 3}{5}

cos (2 x) (sin (x) + \frac{2}{2}) = 0

5 sin (θ) = 5

2 sin (3 x) = 2, 0 \leq x \leq 2 π

7.9615 = 59.2153 cos (x) - 12 sin (x)

What is the general solution for (30)/(sin(x))=(50)/(sin(90)) ?
The general solution for (30)/(sin(x))=(50)/(sin(90)) is x=0.64350…+360n,x=180-0.64350…+360n