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

Radians

a = 0.50535 \dots + 2 πn, a = π - 0.50535 \dots + 2 πn

Solution steps

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

Cross multiply

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

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

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

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

Divide both sides by

4

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

Divide both sides by

4

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

Simplify

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

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

Verify Solutions

Find undefined (singularity) points:

sin (a) = 0

Take the denominator(s) of

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

Apply trig inverse properties

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

General solutions for

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

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

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

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