What is the general solution for (sin(25)}{5.41}=\frac{sin(x))/9 ?

The general solution for (sin(25)}{5.41}=\frac{sin(x))/9 is x=0.77969…+360n,x=180-0.77969…+360n

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(sin(25)}{5.41}=\frac{sin(x))/9

\frac{sin ( 2 5 ^{\circ} )}{5.41} = \frac{sin ( x )}{9}

x = 0.77969 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.77969 \dots + 36 0^{\circ} n

Radians

x = 0.77969 \dots + 2 πn, x = π - 0.77969 \dots + 2 πn

Solution steps

\frac{sin ( 2 5 ^{\circ} )}{5.41} = \frac{sin ( x )}{9}

Switch sides

\frac{sin ( x )}{9} = \frac{sin ( 2 5 ^{\circ} )}{5.41}

Multiply both sides by

9

\frac{sin ( x )}{9} = \frac{sin ( 2 5 ^{\circ} )}{5.41}

Multiply both sides by

9

\frac{9 sin ( x )}{9} = \frac{9 sin ( 2 5 ^{\circ} )}{5.41}

Simplify

sin (x) = \frac{9 sin ( 2 5 ^{\circ} )}{5.41}

sin (x) = \frac{9 sin ( 2 5 ^{\circ} )}{5.41}

Apply trig inverse properties

sin (x) = \frac{9 sin ( 2 5 ^{\circ} )}{5.41}

General solutions for

sin (x) = \frac{9 sin ( 2 5 ^{\circ} )}{5.41}

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

x = arcsin (\frac{9 sin ( 2 5 ^{\circ} )}{5.41}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{9 sin ( 2 5 ^{\circ} )}{5.41}) + 36 0^{\circ} n

x = arcsin (\frac{9 sin ( 2 5 ^{\circ} )}{5.41}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{9 sin ( 2 5 ^{\circ} )}{5.41}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.77969 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.77969 \dots + 36 0^{\circ} n

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What is the general solution for (sin(25)}{5.41}=\frac{sin(x))/9 ?
The general solution for (sin(25)}{5.41}=\frac{sin(x))/9 is x=0.77969…+360n,x=180-0.77969…+360n