What is the general solution for (20)/(sin(35))=(16)/(sin(C)) ?

The general solution for (20)/(sin(35))=(16)/(sin(C)) is C=0.47671…+360n,C=180-0.47671…+360n

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(20)/(sin(35))=(16)/(sin(C))

\frac{20}{sin ( 3 5 ^{\circ} )} = \frac{16}{sin ( C )}

C = 0.47671 \dots + 36 0^{\circ} n, C = 18 0^{\circ} - 0.47671 \dots + 36 0^{\circ} n

Radians

C = 0.47671 \dots + 2 πn, C = π - 0.47671 \dots + 2 πn

Solution steps

\frac{20}{sin ( 3 5 ^{\circ} )} = \frac{16}{sin ( C )}

Cross multiply

\frac{20}{sin ( 3 5 ^{\circ} )} = \frac{16}{sin ( C )}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

20 sin (C) = sin (3 5^{\circ}) \cdot 16

20 sin (C) = sin (3 5^{\circ}) \cdot 16

Divide both sides by

20

20 sin (C) = sin (3 5^{\circ}) \cdot 16

Divide both sides by

20

\frac{20 sin ( C )}{20} = \frac{sin ( 3 5 ^{\circ} ) \cdot 16}{20}

Simplify

sin (C) = \frac{4 sin ( 3 5 ^{\circ} )}{5}

sin (C) = \frac{4 sin ( 3 5 ^{\circ} )}{5}

Verify Solutions

Find undefined (singularity) points:

sin (C) = 0

Take the denominator(s) of

\frac{16}{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{4 sin ( 3 5 ^{\circ} )}{5}

Apply trig inverse properties

sin (C) = \frac{4 sin ( 3 5 ^{\circ} )}{5}

General solutions for

sin (C) = \frac{4 sin ( 3 5 ^{\circ} )}{5}

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

C = arcsin (\frac{4 sin ( 3 5 ^{\circ} )}{5}) + 36 0^{\circ} n, C = 18 0^{\circ} - arcsin (\frac{4 sin ( 3 5 ^{\circ} )}{5}) + 36 0^{\circ} n

C = arcsin (\frac{4 sin ( 3 5 ^{\circ} )}{5}) + 36 0^{\circ} n, C = 18 0^{\circ} - arcsin (\frac{4 sin ( 3 5 ^{\circ} )}{5}) + 36 0^{\circ} n

Show solutions in decimal form

C = 0.47671 \dots + 36 0^{\circ} n, C = 18 0^{\circ} - 0.47671 \dots + 36 0^{\circ} n

\frac{tan ( 2 θ )}{2} = tan (θ)

2 sin^{2} (3 x) - 3 cos (3 x) + 1 = 0, 0^{\circ} \leq x \leq 18 0^{\circ}

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

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

12 sin (A) + 4 = 4 sin (A) + 4

What is the general solution for (20)/(sin(35))=(16)/(sin(C)) ?
The general solution for (20)/(sin(35))=(16)/(sin(C)) is C=0.47671…+360n,C=180-0.47671…+360n