What is the general solution for (sin(x))/5 =(sin(125))/(20) ?

The general solution for (sin(x))/5 =(sin(125))/(20) is x=0.20624…+360n,x=180-0.20624…+360n

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(sin(x))/5 =(sin(125))/(20)

\frac{sin ( x )}{5} = \frac{sin ( 12 5 ^{\circ} )}{20}

x = 0.20624 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.20624 \dots + 36 0^{\circ} n

Solution steps

\frac{sin ( x )}{5} = \frac{sin ( 12 5 ^{\circ} )}{20}

Multiply both sides by

10

2 sin (x) = \frac{sin ( 12 5 ^{\circ} )}{2}

Divide both sides by

2

sin (x) = \frac{sin ( 12 5 ^{\circ} )}{4}

Apply trig inverse properties

x = arcsin (\frac{sin ( 12 5 ^{\circ} )}{4}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{sin ( 12 5 ^{\circ} )}{4}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.20624 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.20624 \dots + 36 0^{\circ} n

tan (\frac{8 x + 1 ^{\circ}}{5}) \cdot cot (\frac{x + 7 ^{\circ}}{2}) = 1

sin (4 t) cos (t) = sin (t) cos (4 t)

3 tan (3 x + \frac{π}{2}) + 1 = 0

- 2 sin (x) - 2 cos (x) = 0

7 sin (b) = 5 sin (7 0^{\circ})

What is the general solution for (sin(x))/5 =(sin(125))/(20) ?
The general solution for (sin(x))/5 =(sin(125))/(20) is x=0.20624…+360n,x=180-0.20624…+360n