What is the general solution for (30)/(sin(A))=(34.4)/(sin(62)) ?

The general solution for (30)/(sin(A))=(34.4)/(sin(62)) is A=0.87886…+360n,A=180-0.87886…+360n

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(30)/(sin(A))=(34.4)/(sin(62))

\frac{30}{sin ( A )} = \frac{34.4}{sin ( 6 2 ^{\circ} )}

A = 0.87886 \dots + 36 0^{\circ} n, A = 18 0^{\circ} - 0.87886 \dots + 36 0^{\circ} n

Radians

A = 0.87886 \dots + 2 πn, A = π - 0.87886 \dots + 2 πn

Solution steps

\frac{30}{sin ( A )} = \frac{34.4}{sin ( 6 2 ^{\circ} )}

Cross multiply

\frac{30}{sin ( A )} = \frac{34.4}{sin ( 6 2 ^{\circ} )}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

30 sin (6 2^{\circ}) = sin (A) \cdot 34.4

30 sin (6 2^{\circ}) = sin (A) \cdot 34.4

Switch sides

sin (A) \cdot 34.4 = 30 sin (6 2^{\circ})

Divide both sides by

34.4

sin (A) \cdot 34.4 = 30 sin (6 2^{\circ})

Divide both sides by

34.4

\frac{sin ( A ) \cdot 34.4}{34.4} = \frac{30 sin ( 6 2 ^{\circ} )}{34.4}

Simplify

sin (A) = \frac{30 sin ( 6 2 ^{\circ} )}{34.4}

sin (A) = \frac{30 sin ( 6 2 ^{\circ} )}{34.4}

Verify Solutions

Find undefined (singularity) points:

sin (A) = 0

Take the denominator(s) of

\frac{30}{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{30 sin ( 6 2 ^{\circ} )}{34.4}

Apply trig inverse properties

sin (A) = \frac{30 sin ( 6 2 ^{\circ} )}{34.4}

General solutions for

sin (A) = \frac{30 sin ( 6 2 ^{\circ} )}{34.4}

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

A = arcsin (\frac{30 sin ( 6 2 ^{\circ} )}{34.4}) + 36 0^{\circ} n, A = 18 0^{\circ} - arcsin (\frac{30 sin ( 6 2 ^{\circ} )}{34.4}) + 36 0^{\circ} n

A = arcsin (\frac{30 sin ( 6 2 ^{\circ} )}{34.4}) + 36 0^{\circ} n, A = 18 0^{\circ} - arcsin (\frac{30 sin ( 6 2 ^{\circ} )}{34.4}) + 36 0^{\circ} n

Show solutions in decimal form

A = 0.87886 \dots + 36 0^{\circ} n, A = 18 0^{\circ} - 0.87886 \dots + 36 0^{\circ} n

- 2 sin (x) = 1

- 5 sin (x) = - 2 cos^{2} (x) + 4, 0 \leq x \leq 2 π

6 = sin (\frac{π}{4} x) + 5

2 cos (θ) + 1 = 0, 0 \leq θ \leq 2 π

t, 4.6 = 0.106 cos (4.36 t)

What is the general solution for (30)/(sin(A))=(34.4)/(sin(62)) ?
The general solution for (30)/(sin(A))=(34.4)/(sin(62)) is A=0.87886…+360n,A=180-0.87886…+360n