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

Solution steps

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

Cross multiply

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

Verify Solutions

Find undefined (singularity) points:

sin (A) = 0

Combine undefined points with solutions:

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

Apply trig inverse properties

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