What is the general solution for (51)/(sin(93))=(43)/(sin(C)) ?

The general solution for (51)/(sin(93))=(43)/(sin(C)) is C=1.00094…+360n,C=180-1.00094…+360n

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(51)/(sin(93))=(43)/(sin(C))

\frac{51}{sin ( 9 3 ^{\circ} )} = \frac{43}{sin ( C )}

C = 1.00094 \dots + 36 0^{\circ} n, C = 18 0^{\circ} - 1.00094 \dots + 36 0^{\circ} n

Radians

C = 1.00094 \dots + 2 πn, C = π - 1.00094 \dots + 2 πn

Solution steps

\frac{51}{sin ( 9 3 ^{\circ} )} = \frac{43}{sin ( C )}

Cross multiply

\frac{51}{sin ( 9 3 ^{\circ} )} = \frac{43}{sin ( C )}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

51 sin (C) = sin (9 3^{\circ}) \cdot 43

51 sin (C) = sin (9 3^{\circ}) \cdot 43

Divide both sides by

51

51 sin (C) = sin (9 3^{\circ}) \cdot 43

Divide both sides by

51

\frac{51 sin ( C )}{51} = \frac{sin ( 9 3 ^{\circ} ) \cdot 43}{51}

Simplify

sin (C) = \frac{sin ( 9 3 ^{\circ} ) \cdot 43}{51}

sin (C) = \frac{sin ( 9 3 ^{\circ} ) \cdot 43}{51}

Verify Solutions

Find undefined (singularity) points:

sin (C) = 0

Take the denominator(s) of

\frac{43}{sin ( C )}

and compare to zero

sin (C) = 0

The following points are undefined

sin (C) = 0

Combine undefined points with solutions:

sin (C) = \frac{sin ( 9 3 ^{\circ} ) \cdot 43}{51}

Apply trig inverse properties

sin (C) = \frac{sin ( 9 3 ^{\circ} ) \cdot 43}{51}

General solutions for

sin (C) = \frac{sin ( 9 3 ^{\circ} ) 43}{51}

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

C = arcsin (\frac{sin ( 9 3 ^{\circ} ) \cdot 43}{51}) + 36 0^{\circ} n, C = 18 0^{\circ} - arcsin (\frac{sin ( 9 3 ^{\circ} ) \cdot 43}{51}) + 36 0^{\circ} n

C = arcsin (\frac{sin ( 9 3 ^{\circ} ) \cdot 43}{51}) + 36 0^{\circ} n, C = 18 0^{\circ} - arcsin (\frac{sin ( 9 3 ^{\circ} ) \cdot 43}{51}) + 36 0^{\circ} n

Show solutions in decimal form

C = 1.00094 \dots + 36 0^{\circ} n, C = 18 0^{\circ} - 1.00094 \dots + 36 0^{\circ} n

cos (x) = 16

- \frac{1}{25} + cos^{2} (x) = 1

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

2 cos (3 x) = 1 + cos (x)

2 csc (x) - 2 = 0

What is the general solution for (51)/(sin(93))=(43)/(sin(C)) ?
The general solution for (51)/(sin(93))=(43)/(sin(C)) is C=1.00094…+360n,C=180-1.00094…+360n