What is the general solution for sin(B)=(7sin(36))/(12) ?

The general solution for sin(B)=(7sin(36))/(12) is B=0.34997…+360n,B=180-0.34997…+360n

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sin(B)=(7sin(36))/(12)

sin (B) = \frac{7 sin ( 3 6 ^{\circ} )}{12}

B = 0.34997 \dots + 36 0^{\circ} n, B = 18 0^{\circ} - 0.34997 \dots + 36 0^{\circ} n

Solution steps

sin (B) = \frac{7 sin ( 3 6 ^{\circ} )}{12}

sin (3 6^{\circ}) = \frac{2 5 - 5}{4}

sin (B) = \frac{7 \cdot \frac{2 5 - 5}{4}}{12}

Simplify

\frac{7 \cdot \frac{2 5 - 5}{4}}{12} : \frac{7 2 5 - 5}{48}

Apply trig inverse properties

B = arcsin (\frac{7 2 5 - 5}{48}) + 36 0^{\circ} n, B = 18 0^{\circ} - arcsin (\frac{7 2 5 - 5}{48}) + 36 0^{\circ} n

Show solutions in decimal form

B = 0.34997 \dots + 36 0^{\circ} n, B = 18 0^{\circ} - 0.34997 \dots + 36 0^{\circ} n

x, cos^{2} (x) = sin (y + \frac{π}{2})

0 = (sin (x))^{2}

sec^{2} (x) - tan^{2} (x) = cos (x)

x, cos^{2} (x) - sin^{2} (x) = 0

cos (x) = \frac{60}{61}, cos (2 x)

What is the general solution for sin(B)=(7sin(36))/(12) ?
The general solution for sin(B)=(7sin(36))/(12) is B=0.34997…+360n,B=180-0.34997…+360n