What is the general solution for (15)/(sin(32))=(12)/(sin(b)) ?

The general solution for (15)/(sin(32))=(12)/(sin(b)) is b=0.43778…+360n,b=180-0.43778…+360n

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(15)/(sin(32))=(12)/(sin(b))

\frac{15}{sin ( 3 2 ^{\circ} )} = \frac{12}{sin ( b )}

b = 0.43778 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.43778 \dots + 36 0^{\circ} n

Solution steps

\frac{15}{sin ( 3 2 ^{\circ} )} = \frac{12}{sin ( b )}

Cross multiply

15 sin (b) = sin (3 2^{\circ}) \cdot 12

Divide both sides by

15

sin (b) = \frac{4 sin ( 3 2 ^{\circ} )}{5}

Verify Solutions

Find undefined (singularity) points:

sin (b) = 0

Combine undefined points with solutions:

sin (b) = \frac{4 sin ( 3 2 ^{\circ} )}{5}

Apply trig inverse properties

b = arcsin (\frac{4 sin ( 3 2 ^{\circ} )}{5}) + 36 0^{\circ} n, b = 18 0^{\circ} - arcsin (\frac{4 sin ( 3 2 ^{\circ} )}{5}) + 36 0^{\circ} n

Show solutions in decimal form

b = 0.43778 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.43778 \dots + 36 0^{\circ} n

\frac{sin ( x )}{25} = \frac{sin ( 12 5 ^{\circ} )}{165.6}

2 cos (3 θ) - 1 = 0

cos (4 x) = cos (8 x)

cos (2 x) - cos (x) = 2

4 sin (2 x) + 23 = 0

What is the general solution for (15)/(sin(32))=(12)/(sin(b)) ?
The general solution for (15)/(sin(32))=(12)/(sin(b)) is b=0.43778…+360n,b=180-0.43778…+360n