What is the general solution for 8/(sin(38))= 6/(sin(a)) ?

The general solution for 8/(sin(38))= 6/(sin(a)) is a=0.47996…+360n,a=180-0.47996…+360n

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8/(sin(38))= 6/(sin(a))

\frac{8}{sin ( 3 8 ^{\circ} )} = \frac{6}{sin ( a )}

a = 0.47996 \dots + 36 0^{\circ} n, a = 18 0^{\circ} - 0.47996 \dots + 36 0^{\circ} n

Radians

a = 0.47996 \dots + 2 πn, a = π - 0.47996 \dots + 2 πn

Solution steps

\frac{8}{sin ( 3 8 ^{\circ} )} = \frac{6}{sin ( a )}

Cross multiply

\frac{8}{sin ( 3 8 ^{\circ} )} = \frac{6}{sin ( a )}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

8 sin (a) = sin (3 8^{\circ}) \cdot 6

8 sin (a) = sin (3 8^{\circ}) \cdot 6

Divide both sides by

8

8 sin (a) = sin (3 8^{\circ}) \cdot 6

Divide both sides by

8

\frac{8 sin ( a )}{8} = \frac{sin ( 3 8 ^{\circ} ) \cdot 6}{8}

Simplify

sin (a) = \frac{3 sin ( 3 8 ^{\circ} )}{4}

sin (a) = \frac{3 sin ( 3 8 ^{\circ} )}{4}

Verify Solutions

Find undefined (singularity) points:

sin (a) = 0

Take the denominator(s) of

\frac{6}{sin ( a )}

and compare to zero

sin (a) = 0

The following points are undefined

sin (a) = 0

Combine undefined points with solutions:

sin (a) = \frac{3 sin ( 3 8 ^{\circ} )}{4}

Apply trig inverse properties

sin (a) = \frac{3 sin ( 3 8 ^{\circ} )}{4}

General solutions for

sin (a) = \frac{3 sin ( 3 8 ^{\circ} )}{4}

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

a = arcsin (\frac{3 sin ( 3 8 ^{\circ} )}{4}) + 36 0^{\circ} n, a = 18 0^{\circ} - arcsin (\frac{3 sin ( 3 8 ^{\circ} )}{4}) + 36 0^{\circ} n

a = arcsin (\frac{3 sin ( 3 8 ^{\circ} )}{4}) + 36 0^{\circ} n, a = 18 0^{\circ} - arcsin (\frac{3 sin ( 3 8 ^{\circ} )}{4}) + 36 0^{\circ} n

Show solutions in decimal form

a = 0.47996 \dots + 36 0^{\circ} n, a = 18 0^{\circ} - 0.47996 \dots + 36 0^{\circ} n

What is the general solution for 8/(sin(38))= 6/(sin(a)) ?
The general solution for 8/(sin(38))= 6/(sin(a)) is a=0.47996…+360n,a=180-0.47996…+360n