What is the general solution for (10)/(sin(30))= 3/(sin(b)) ?

The general solution for (10)/(sin(30))= 3/(sin(b)) is b=0.15056…+360n,b=180-0.15056…+360n

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(10)/(sin(30))= 3/(sin(b))

\frac{10}{sin ( 3 0 ^{\circ} )} = \frac{3}{sin ( b )}

b = 0.15056 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.15056 \dots + 36 0^{\circ} n

Solution steps

\frac{10}{sin ( 3 0 ^{\circ} )} = \frac{3}{sin ( b )}

sin (3 0^{\circ}) = \frac{1}{2}

\frac{10}{\frac{1}{2}} = \frac{3}{sin ( b )}

Cross multiply

10 sin (b) = \frac{3}{2}

Divide both sides by

10

sin (b) = \frac{3}{20}

Verify Solutions

Find undefined (singularity) points:

sin (b) = 0

Combine undefined points with solutions:

sin (b) = \frac{3}{20}

Apply trig inverse properties

b = arcsin (\frac{3}{20}) + 36 0^{\circ} n, b = 18 0^{\circ} - arcsin (\frac{3}{20}) + 36 0^{\circ} n

Show solutions in decimal form

b = 0.15056 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.15056 \dots + 36 0^{\circ} n

tan (\frac{θ}{2} - \frac{π}{6}) = - 1, 0 \leq θ < 2 π

arctan (x + 2) - arctan (x + 1) = \frac{π}{4}

3 cos (2 x) = 1

cos^{2} (x) = (1 + sin (x)) (1 - cos (x))

tan (x) = 1, - π < x \leq π

What is the general solution for (10)/(sin(30))= 3/(sin(b)) ?
The general solution for (10)/(sin(30))= 3/(sin(b)) is b=0.15056…+360n,b=180-0.15056…+360n