What is the general solution for (6.7)/(sin(33))=(5.4)/(sin(A)) ?

The general solution for (6.7)/(sin(33))=(5.4)/(sin(A)) is A=0.45444…+360n,A=180-0.45444…+360n

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(6.7)/(sin(33))=(5.4)/(sin(A))

\frac{6.7}{sin ( 3 3 ^{\circ} )} = \frac{5.4}{sin ( A )}

A = 0.45444 \dots + 36 0^{\circ} n, A = 18 0^{\circ} - 0.45444 \dots + 36 0^{\circ} n

Radians

A = 0.45444 \dots + 2 πn, A = π - 0.45444 \dots + 2 πn

Solution steps

\frac{6.7}{sin ( 3 3 ^{\circ} )} = \frac{5.4}{sin ( A )}

Cross multiply

\frac{6.7}{sin ( 3 3 ^{\circ} )} = \frac{5.4}{sin ( A )}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

6.7 sin (A) = sin (3 3^{\circ}) \cdot 5.4

6.7 sin (A) = sin (3 3^{\circ}) \cdot 5.4

Divide both sides by

6.7

6.7 sin (A) = sin (3 3^{\circ}) \cdot 5.4

Divide both sides by

6.7

\frac{6.7 sin ( A )}{6.7} = \frac{sin ( 3 3 ^{\circ} ) \cdot 5.4}{6.7}

Simplify

sin (A) = \frac{sin ( 3 3 ^{\circ} ) \cdot 5.4}{6.7}

sin (A) = \frac{sin ( 3 3 ^{\circ} ) \cdot 5.4}{6.7}

Verify Solutions

Find undefined (singularity) points:

sin (A) = 0

Take the denominator(s) of

\frac{5.4}{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 ( 3 3 ^{\circ} ) \cdot 5.4}{6.7}

Apply trig inverse properties

sin (A) = \frac{sin ( 3 3 ^{\circ} ) \cdot 5.4}{6.7}

General solutions for

sin (A) = \frac{sin ( 3 3 ^{\circ} ) 5.4}{6.7}

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 ( 3 3 ^{\circ} ) \cdot 5.4}{6.7}) + 36 0^{\circ} n, A = 18 0^{\circ} - arcsin (\frac{sin ( 3 3 ^{\circ} ) \cdot 5.4}{6.7}) + 36 0^{\circ} n

A = arcsin (\frac{sin ( 3 3 ^{\circ} ) \cdot 5.4}{6.7}) + 36 0^{\circ} n, A = 18 0^{\circ} - arcsin (\frac{sin ( 3 3 ^{\circ} ) \cdot 5.4}{6.7}) + 36 0^{\circ} n

Show solutions in decimal form

A = 0.45444 \dots + 36 0^{\circ} n, A = 18 0^{\circ} - 0.45444 \dots + 36 0^{\circ} n

2 - 3 sin (θ) = 0

cos (x) = - 0.83

y, x = cot (y)

x, 2 cos (\frac{π x}{3}) = 1

cos (x) = - 0.16

What is the general solution for (6.7)/(sin(33))=(5.4)/(sin(A)) ?
The general solution for (6.7)/(sin(33))=(5.4)/(sin(A)) is A=0.45444…+360n,A=180-0.45444…+360n