What is the general solution for 8/(sin(45))=(42)/(sin(x)) ?

The general solution for 8/(sin(45))=(42)/(sin(x)) is No Solution for x\in\mathbb{R}

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8/(sin(45))=(42)/(sin(x))

\frac{8}{sin ( 4 5 ^{\circ} )} = \frac{42}{sin ( x )}

No Solution for x \in R

Solution steps

\frac{8}{sin ( 4 5 ^{\circ} )} = \frac{42}{sin ( x )}

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

Use the following trivial identity:

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

= \frac{2}{2}

\frac{8}{\frac{2}{2}} = \frac{42}{sin ( x )}

Cross multiply

\frac{8}{\frac{2}{2}} = \frac{42}{sin ( x )}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

8 sin (x) = \frac{2}{2} \cdot 42

Simplify

\frac{2}{2} \cdot 42 : 212

\frac{2}{2} \cdot 42

Multiply fractions:

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

= \frac{2 \cdot 42}{2}

Divide the numbers:

\frac{42}{2} = 21

= 212

8 sin (x) = 212

8 sin (x) = 212

Divide both sides by

8

8 sin (x) = 212

Divide both sides by

8

\frac{8 sin ( x )}{8} = \frac{21 2}{8}

Simplify

sin (x) = \frac{21 2}{8}

sin (x) = \frac{21 2}{8}

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Take the denominator(s) of

\frac{42}{sin ( x )}

and compare to zero

sin (x) = 0

The following points are undefined

sin (x) = 0

Combine undefined points with solutions:

sin (x) = \frac{21 2}{8}

- 1 \leq sin (x) \leq 1

No Solution for x \in R

What is the general solution for 8/(sin(45))=(42)/(sin(x)) ?
The general solution for 8/(sin(45))=(42)/(sin(x)) is No Solution for x\in\mathbb{R}