What is the general solution for (37)/(sin(x))=(30)/(sin(30)) ?

The general solution for (37)/(sin(x))=(30)/(sin(30)) is x=0.66450…+360n,x=180-0.66450…+360n

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(37)/(sin(x))=(30)/(sin(30))

\frac{37}{sin ( x )} = \frac{30}{sin ( 3 0 ^{\circ} )}

x = 0.66450 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.66450 \dots + 36 0^{\circ} n

Solution steps

\frac{37}{sin ( x )} = \frac{30}{sin ( 3 0 ^{\circ} )}

sin (3 0^{\circ}) = \frac{1}{2}

\frac{37}{sin ( x )} = \frac{30}{\frac{1}{2}}

Cross multiply

\frac{37}{2} = sin (x) \cdot 30

Switch sides

sin (x) \cdot 30 = \frac{37}{2}

Divide both sides by

30

sin (x) = \frac{37}{60}

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Combine undefined points with solutions:

sin (x) = \frac{37}{60}

Apply trig inverse properties

x = arcsin (\frac{37}{60}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{37}{60}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.66450 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.66450 \dots + 36 0^{\circ} n

\frac{1}{cos ( θ )} = 1

\frac{sin ( x ) + cos ( x )}{sin ( x )} = \frac{1 + 1}{tan ( x )}

3 tan (x + 4 5^{\circ}) = 3

0 = sin (π x)

sec (θ) csc (θ) = 1

What is the general solution for (37)/(sin(x))=(30)/(sin(30)) ?
The general solution for (37)/(sin(x))=(30)/(sin(30)) is x=0.66450…+360n,x=180-0.66450…+360n