What is the general solution for (sin(112.8))/(16.1)=(sin(x))/(12.2) ?

The general solution for (sin(112.8))/(16.1)=(sin(x))/(12.2) is x=0.77337…+360n,x=180-0.77337…+360n

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(sin(112.8))/(16.1)=(sin(x))/(12.2)

\frac{sin ( 112. 8 ^{\circ} )}{16.1} = \frac{sin ( x )}{12.2}

x = 0.77337 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.77337 \dots + 36 0^{\circ} n

Radians

x = 0.77337 \dots + 2 πn, x = π - 0.77337 \dots + 2 πn

Solution steps

\frac{sin ( 112. 8 ^{\circ} )}{16.1} = \frac{sin ( x )}{12.2}

Switch sides

\frac{sin ( x )}{12.2} = \frac{sin ( 112. 8 ^{\circ} )}{16.1}

Multiply both sides by

12.2

\frac{sin ( x )}{12.2} = \frac{sin ( 112. 8 ^{\circ} )}{16.1}

Multiply both sides by

12.2

\frac{12.2 sin ( x )}{12.2} = \frac{12.2 sin ( 112. 8 ^{\circ} )}{16.1}

Simplify

sin (x) = \frac{12.2 sin ( 112. 8 ^{\circ} )}{16.1}

sin (x) = \frac{12.2 sin ( 112. 8 ^{\circ} )}{16.1}

Apply trig inverse properties

sin (x) = \frac{12.2 sin ( 112. 8 ^{\circ} )}{16.1}

General solutions for

sin (x) = \frac{12.2 sin ( 112. 8 ^{\circ} )}{16.1}

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

x = arcsin (\frac{12.2 sin ( 112. 8 ^{\circ} )}{16.1}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{12.2 sin ( 112. 8 ^{\circ} )}{16.1}) + 36 0^{\circ} n

x = arcsin (\frac{12.2 sin ( 112. 8 ^{\circ} )}{16.1}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{12.2 sin ( 112. 8 ^{\circ} )}{16.1}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.77337 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.77337 \dots + 36 0^{\circ} n

(sin (x) + cos (x))^{2} = \frac{3}{2}

2 sin^{2} (t) - sin (t) - 1 = 0

cos (x) = - \frac{1}{5 2}

cot (x) tan (2 x) = 3

2 cos^{2} (x) - 3 cos (x) = 0

What is the general solution for (sin(112.8))/(16.1)=(sin(x))/(12.2) ?
The general solution for (sin(112.8))/(16.1)=(sin(x))/(12.2) is x=0.77337…+360n,x=180-0.77337…+360n