What is the general solution for (sin(47))/(12)=(sin(x))/(11) ?

The general solution for (sin(47))/(12)=(sin(x))/(11) is x=0.73475…+360n,x=180-0.73475…+360n

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(sin(47))/(12)=(sin(x))/(11)

\frac{sin ( 4 7 ^{\circ} )}{12} = \frac{sin ( x )}{11}

x = 0.73475 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.73475 \dots + 36 0^{\circ} n

Solution steps

\frac{sin ( 4 7 ^{\circ} )}{12} = \frac{sin ( x )}{11}

Switch sides

\frac{sin ( x )}{11} = \frac{sin ( 4 7 ^{\circ} )}{12}

Multiply both sides by

11

sin (x) = \frac{11 sin ( 4 7 ^{\circ} )}{12}

Apply trig inverse properties

x = arcsin (\frac{11 sin ( 4 7 ^{\circ} )}{12}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{11 sin ( 4 7 ^{\circ} )}{12}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.73475 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.73475 \dots + 36 0^{\circ} n

cos (2 x) + 3 cos (x) = - 1

2 cos (α) = 3

(csc (θ) + 2) (3 cot (θ) + 3) = 0

3 tan (x) - 2 sin (x) = 0

2 sin^{2} (2 x) - cos (2 x) - 1 = 0

What is the general solution for (sin(47))/(12)=(sin(x))/(11) ?
The general solution for (sin(47))/(12)=(sin(x))/(11) is x=0.73475…+360n,x=180-0.73475…+360n