What is the general solution for (sin(40))/8 =(sin(x))/(12) ?

The general solution for (sin(40))/8 =(sin(x))/(12) is x=1.30233…+360n,x=180-1.30233…+360n

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(sin(40))/8 =(sin(x))/(12)

\frac{sin ( 4 0 ^{\circ} )}{8} = \frac{sin ( x )}{12}

x = 1.30233 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.30233 \dots + 36 0^{\circ} n

Radians

x = 1.30233 \dots + 2 πn, x = π - 1.30233 \dots + 2 πn

Solution steps

\frac{sin ( 4 0 ^{\circ} )}{8} = \frac{sin ( x )}{12}

Switch sides

\frac{sin ( x )}{12} = \frac{sin ( 4 0 ^{\circ} )}{8}

Multiply both sides by

12

\frac{sin ( x )}{12} = \frac{sin ( 4 0 ^{\circ} )}{8}

Multiply both sides by

12

\frac{12 sin ( x )}{12} = \frac{12 sin ( 4 0 ^{\circ} )}{8}

Simplify

sin (x) = \frac{3 sin ( 4 0 ^{\circ} )}{2}

sin (x) = \frac{3 sin ( 4 0 ^{\circ} )}{2}

Apply trig inverse properties

sin (x) = \frac{3 sin ( 4 0 ^{\circ} )}{2}

General solutions for

sin (x) = \frac{3 sin ( 4 0 ^{\circ} )}{2}

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

x = arcsin (\frac{3 sin ( 4 0 ^{\circ} )}{2}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{3 sin ( 4 0 ^{\circ} )}{2}) + 36 0^{\circ} n

x = arcsin (\frac{3 sin ( 4 0 ^{\circ} )}{2}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{3 sin ( 4 0 ^{\circ} )}{2}) + 36 0^{\circ} n

Show solutions in decimal form

x = 1.30233 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.30233 \dots + 36 0^{\circ} n

y, \frac{3}{2} = sin (y)

tan (β) = 2, 18 0^{\circ} \leq β \leq 27 0^{\circ}

cos (x) = \frac{1}{3}, cos (2 x)

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

x, sin (x) \cdot cos (y) = 0

What is the general solution for (sin(40))/8 =(sin(x))/(12) ?
The general solution for (sin(40))/8 =(sin(x))/(12) is x=1.30233…+360n,x=180-1.30233…+360n