What is the general solution for 8/(sin(38))= 6/(sin(a)) ?

The general solution for 8/(sin(38))= 6/(sin(a)) is a=0.47996…+360n,a=180-0.47996…+360n

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8/(sin(38))= 6/(sin(a))

\frac{8}{sin ( 3 8 ^{\circ} )} = \frac{6}{sin ( a )}

a = 0.47996 \dots + 36 0^{\circ} n, a = 18 0^{\circ} - 0.47996 \dots + 36 0^{\circ} n

Solution steps

\frac{8}{sin ( 3 8 ^{\circ} )} = \frac{6}{sin ( a )}

Cross multiply

8 sin (a) = sin (3 8^{\circ}) \cdot 6

Divide both sides by

8

sin (a) = \frac{3 sin ( 3 8 ^{\circ} )}{4}

Verify Solutions

Find undefined (singularity) points:

sin (a) = 0

Combine undefined points with solutions:

sin (a) = \frac{3 sin ( 3 8 ^{\circ} )}{4}

Apply trig inverse properties

a = arcsin (\frac{3 sin ( 3 8 ^{\circ} )}{4}) + 36 0^{\circ} n, a = 18 0^{\circ} - arcsin (\frac{3 sin ( 3 8 ^{\circ} )}{4}) + 36 0^{\circ} n

Show solutions in decimal form

a = 0.47996 \dots + 36 0^{\circ} n, a = 18 0^{\circ} - 0.47996 \dots + 36 0^{\circ} n

28 cos (θ) = 4, 0^{\circ} \leq θ < 36 0^{\circ}

6 sin (θ) + 2 = sin (θ)

cos (θ) = - \frac{19}{17}

5 = 7 - cos (θ) + 5 cos (2 θ)

tan (2 x) = 0.32

What is the general solution for 8/(sin(38))= 6/(sin(a)) ?
The general solution for 8/(sin(38))= 6/(sin(a)) is a=0.47996…+360n,a=180-0.47996…+360n