What is the general solution for (sin(x))/(25)=(sin(125))/(165.6) ?

The general solution for (sin(x))/(25)=(sin(125))/(165.6) is x=0.12398…+360n,x=180-0.12398…+360n

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(sin(x))/(25)=(sin(125))/(165.6)

\frac{sin ( x )}{25} = \frac{sin ( 12 5 ^{\circ} )}{165.6}

x = 0.12398 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.12398 \dots + 36 0^{\circ} n

Radians

x = 0.12398 \dots + 2 πn, x = π - 0.12398 \dots + 2 πn

Solution steps

\frac{sin ( x )}{25} = \frac{sin ( 12 5 ^{\circ} )}{165.6}

Multiply both sides by

25

\frac{sin ( x )}{25} = \frac{sin ( 12 5 ^{\circ} )}{165.6}

Multiply both sides by

25

\frac{25 sin ( x )}{25} = \frac{25 sin ( 12 5 ^{\circ} )}{165.6}

Simplify

sin (x) = \frac{25 sin ( 12 5 ^{\circ} )}{165.6}

sin (x) = \frac{25 sin ( 12 5 ^{\circ} )}{165.6}

Apply trig inverse properties

sin (x) = \frac{25 sin ( 12 5 ^{\circ} )}{165.6}

General solutions for

sin (x) = \frac{25 sin ( 12 5 ^{\circ} )}{165.6}

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

x = arcsin (\frac{25 sin ( 12 5 ^{\circ} )}{165.6}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{25 sin ( 12 5 ^{\circ} )}{165.6}) + 36 0^{\circ} n

x = arcsin (\frac{25 sin ( 12 5 ^{\circ} )}{165.6}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{25 sin ( 12 5 ^{\circ} )}{165.6}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.12398 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.12398 \dots + 36 0^{\circ} n

2 cos (3 θ) - 1 = 0

cos (4 x) = cos (8 x)

cos (2 x) - cos (x) = 2

4 sin (2 x) + 23 = 0

x, 3 = 18 cos (x)

What is the general solution for (sin(x))/(25)=(sin(125))/(165.6) ?
The general solution for (sin(x))/(25)=(sin(125))/(165.6) is x=0.12398…+360n,x=180-0.12398…+360n