What is the general solution for 4/(sin(104.48))= 2/(sin(a)) ?

The general solution for 4/(sin(104.48))= 2/(sin(a)) is a=0.50535…+360n,a=180-0.50535…+360n

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4/(sin(104.48))= 2/(sin(a))

\frac{4}{sin ( 104.4 8 ^{\circ} )} = \frac{2}{sin ( a )}

a = 0.50535 \dots + 36 0^{\circ} n, a = 18 0^{\circ} - 0.50535 \dots + 36 0^{\circ} n

Solution steps

\frac{4}{sin ( 104.4 8 ^{\circ} )} = \frac{2}{sin ( a )}

Cross multiply

4 sin (a) = sin (104.4 8^{\circ}) \cdot 2

Divide both sides by

4

sin (a) = \frac{sin ( 104.4 8 ^{\circ} )}{2}

Verify Solutions

Find undefined (singularity) points:

sin (a) = 0

Combine undefined points with solutions:

sin (a) = \frac{sin ( 104.4 8 ^{\circ} )}{2}

Apply trig inverse properties

a = arcsin (\frac{sin ( 104.4 8 ^{\circ} )}{2}) + 36 0^{\circ} n, a = 18 0^{\circ} - arcsin (\frac{sin ( 104.4 8 ^{\circ} )}{2}) + 36 0^{\circ} n

Show solutions in decimal form

a = 0.50535 \dots + 36 0^{\circ} n, a = 18 0^{\circ} - 0.50535 \dots + 36 0^{\circ} n

sin (x + \frac{3 π}{2}) - cos (x + \frac{π}{2}) = 1

csc (x) - cot (x) = 1

sin (x) = - \frac{1}{2} sin (2 x)

cot (2 x) = 1.732

sin (9 0^{\circ} - a) = \frac{1}{1.63}

What is the general solution for 4/(sin(104.48))= 2/(sin(a)) ?
The general solution for 4/(sin(104.48))= 2/(sin(a)) is a=0.50535…+360n,a=180-0.50535…+360n