What is the general solution for (sin(12))/(sin(x))= 343/1484 ?

The general solution for (sin(12))/(sin(x))= 343/1484 is x=1.11870…+360n,x=180-1.11870…+360n

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(sin(12))/(sin(x))= 343/1484

\frac{sin ( 1 2 ^{\circ} )}{sin ( x )} = \frac{343}{1484}

x = 1.11870 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.11870 \dots + 36 0^{\circ} n

Radians

x = 1.11870 \dots + 2 πn, x = π - 1.11870 \dots + 2 πn

Solution steps

\frac{sin ( 1 2 ^{\circ} )}{sin ( x )} = \frac{343}{1484}

Cross multiply

\frac{sin ( 1 2 ^{\circ} )}{sin ( x )} = \frac{343}{1484}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

sin (1 2^{\circ}) \cdot 1484 = sin (x) \cdot 343

sin (1 2^{\circ}) \cdot 1484 = sin (x) \cdot 343

Switch sides

sin (x) \cdot 343 = sin (1 2^{\circ}) \cdot 1484

Divide both sides by

343

sin (x) \cdot 343 = sin (1 2^{\circ}) \cdot 1484

Divide both sides by

343

\frac{sin ( x ) \cdot 343}{343} = \frac{sin ( 1 2 ^{\circ} ) \cdot 1484}{343}

Simplify

sin (x) = \frac{212 sin ( 1 2 ^{\circ} )}{49}

sin (x) = \frac{212 sin ( 1 2 ^{\circ} )}{49}

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Take the denominator(s) of

\frac{sin ( 1 2 ^{\circ} )}{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{212 sin ( 1 2 ^{\circ} )}{49}

Apply trig inverse properties

sin (x) = \frac{212 sin ( 1 2 ^{\circ} )}{49}

General solutions for

sin (x) = \frac{212 sin ( 1 2 ^{\circ} )}{49}

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

x = arcsin (\frac{212 sin ( 1 2 ^{\circ} )}{49}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{212 sin ( 1 2 ^{\circ} )}{49}) + 36 0^{\circ} n

x = arcsin (\frac{212 sin ( 1 2 ^{\circ} )}{49}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{212 sin ( 1 2 ^{\circ} )}{49}) + 36 0^{\circ} n

Show solutions in decimal form

x = 1.11870 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.11870 \dots + 36 0^{\circ} n

2 sin (x) - 3 cos (x) = 3

sin (x) = - 0.42

sin (x) = - 0.75

sin (x) = - 0.95

cos^{2} (\frac{x}{2}) = 1

What is the general solution for (sin(12))/(sin(x))= 343/1484 ?
The general solution for (sin(12))/(sin(x))= 343/1484 is x=1.11870…+360n,x=180-1.11870…+360n