What is the general solution for (36)/(sin(110))=(15)/(sin(x)) ?

The general solution for (36)/(sin(110))=(15)/(sin(x)) is x=0.40230…+360n,x=180-0.40230…+360n

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(36)/(sin(110))=(15)/(sin(x))

\frac{36}{sin ( 11 0 ^{\circ} )} = \frac{15}{sin ( x )}

x = 0.40230 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.40230 \dots + 36 0^{\circ} n

Radians

x = 0.40230 \dots + 2 πn, x = π - 0.40230 \dots + 2 πn

Solution steps

\frac{36}{sin ( 11 0 ^{\circ} )} = \frac{15}{sin ( x )}

Cross multiply

\frac{36}{sin ( 11 0 ^{\circ} )} = \frac{15}{sin ( x )}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

36 sin (x) = sin (11 0^{\circ}) \cdot 15

36 sin (x) = sin (11 0^{\circ}) \cdot 15

Divide both sides by

36

36 sin (x) = sin (11 0^{\circ}) \cdot 15

Divide both sides by

36

\frac{36 sin ( x )}{36} = \frac{sin ( 11 0 ^{\circ} ) \cdot 15}{36}

Simplify

sin (x) = \frac{5 sin ( 11 0 ^{\circ} )}{12}

sin (x) = \frac{5 sin ( 11 0 ^{\circ} )}{12}

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Take the denominator(s) of

\frac{15}{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{5 sin ( 11 0 ^{\circ} )}{12}

Apply trig inverse properties

sin (x) = \frac{5 sin ( 11 0 ^{\circ} )}{12}

General solutions for

sin (x) = \frac{5 sin ( 11 0 ^{\circ} )}{12}

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

x = arcsin (\frac{5 sin ( 11 0 ^{\circ} )}{12}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{5 sin ( 11 0 ^{\circ} )}{12}) + 36 0^{\circ} n

x = arcsin (\frac{5 sin ( 11 0 ^{\circ} )}{12}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{5 sin ( 11 0 ^{\circ} )}{12}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.40230 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.40230 \dots + 36 0^{\circ} n

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cos (x) = 0.925

(sin (x) + 1) (2 sin^{2} (x) - 3 sin (x) - 2) = 0

\frac{sin ( A )}{9} = \frac{sin ( 10 8 ^{\circ} )}{6}

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What is the general solution for (36)/(sin(110))=(15)/(sin(x)) ?
The general solution for (36)/(sin(110))=(15)/(sin(x)) is x=0.40230…+360n,x=180-0.40230…+360n