What is the general solution for (sin(31))/(12)=(sin(x))/(16) ?

The general solution for (sin(31))/(12)=(sin(x))/(16) is x=0.75696…+360n,x=180-0.75696…+360n

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(sin(31))/(12)=(sin(x))/(16)

\frac{sin ( 3 1 ^{\circ} )}{12} = \frac{sin ( x )}{16}

x = 0.75696 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.75696 \dots + 36 0^{\circ} n

Radians

x = 0.75696 \dots + 2 πn, x = π - 0.75696 \dots + 2 πn

Solution steps

\frac{sin ( 3 1 ^{\circ} )}{12} = \frac{sin ( x )}{16}

Switch sides

\frac{sin ( x )}{16} = \frac{sin ( 3 1 ^{\circ} )}{12}

Multiply both sides by

16

\frac{sin ( x )}{16} = \frac{sin ( 3 1 ^{\circ} )}{12}

Multiply both sides by

16

\frac{16 sin ( x )}{16} = \frac{16 sin ( 3 1 ^{\circ} )}{12}

Simplify

sin (x) = \frac{4 sin ( 3 1 ^{\circ} )}{3}

sin (x) = \frac{4 sin ( 3 1 ^{\circ} )}{3}

Apply trig inverse properties

sin (x) = \frac{4 sin ( 3 1 ^{\circ} )}{3}

General solutions for

sin (x) = \frac{4 sin ( 3 1 ^{\circ} )}{3}

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

x = arcsin (\frac{4 sin ( 3 1 ^{\circ} )}{3}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{4 sin ( 3 1 ^{\circ} )}{3}) + 36 0^{\circ} n

x = arcsin (\frac{4 sin ( 3 1 ^{\circ} )}{3}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{4 sin ( 3 1 ^{\circ} )}{3}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.75696 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.75696 \dots + 36 0^{\circ} n

tan (θ) = - \frac{8}{6}

cos^{2} (θ) - \frac{3}{2} = \frac{5}{2} cos (θ)

tan (x) = - \frac{1}{8}

sin (x) cot (x) = 1

sin (θ) = 0.4484

What is the general solution for (sin(31))/(12)=(sin(x))/(16) ?
The general solution for (sin(31))/(12)=(sin(x))/(16) is x=0.75696…+360n,x=180-0.75696…+360n