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

Solution steps

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

Cross multiply

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

Divide both sides by

36

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

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Combine undefined points with solutions:

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

Apply trig inverse properties

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

6 sin (\frac{x}{2}) + 6 cos (x) = 0

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}

sin (3 x - 6^{\circ}) = \frac{1}{2}

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