What is the general solution for (120)/(sin(x))=(30)/(sin(8)) ?

The general solution for (120)/(sin(x))=(30)/(sin(8)) is No Solution for x\in\mathbb{R}

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(120)/(sin(x))=(30)/(sin(8))

\frac{120}{sin ( x )} = \frac{30}{sin ( 8 )}

No Solution for x \in R

Solution steps

\frac{120}{sin ( x )} = \frac{30}{sin ( 8 )}

Cross multiply

\frac{120}{sin ( x )} = \frac{30}{sin ( 8 )}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

120 sin (8) = sin (x) \cdot 30

120 sin (8) = sin (x) \cdot 30

Switch sides

sin (x) \cdot 30 = 120 sin (8)

Divide both sides by

30

sin (x) \cdot 30 = 120 sin (8)

Divide both sides by

30

\frac{sin ( x ) \cdot 30}{30} = \frac{120 sin ( 8 )}{30}

Simplify

sin (x) = 4 sin (8)

sin (x) = 4 sin (8)

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Take the denominator(s) of

\frac{120}{sin ( x )}

and compare to zero

sin (x) = 0

The following points are undefined

sin (x) = 0

Combine undefined points with solutions:

sin (x) = 4 sin (8)

- 1 \leq sin (x) \leq 1

No Solution for x \in R

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What is the general solution for (120)/(sin(x))=(30)/(sin(8)) ?
The general solution for (120)/(sin(x))=(30)/(sin(8)) is No Solution for x\in\mathbb{R}