What is the general solution for (408.4)/(sin(130))=(200)/(sin(x)) ?

The general solution for (408.4)/(sin(130))=(200)/(sin(x)) is x=0.38455…+360n,x=180-0.38455…+360n

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(408.4)/(sin(130))=(200)/(sin(x))

\frac{408.4}{sin ( 13 0 ^{\circ} )} = \frac{200}{sin ( x )}

x = 0.38455 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.38455 \dots + 36 0^{\circ} n

Radians

x = 0.38455 \dots + 2 πn, x = π - 0.38455 \dots + 2 πn

Solution steps

\frac{408.4}{sin ( 13 0 ^{\circ} )} = \frac{200}{sin ( x )}

Cross multiply

\frac{408.4}{sin ( 13 0 ^{\circ} )} = \frac{200}{sin ( x )}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

408.4 sin (x) = sin (13 0^{\circ}) \cdot 200

408.4 sin (x) = sin (13 0^{\circ}) \cdot 200

Divide both sides by

408.4

408.4 sin (x) = sin (13 0^{\circ}) \cdot 200

Divide both sides by

408.4

\frac{408.4 sin ( x )}{408.4} = \frac{sin ( 13 0 ^{\circ} ) \cdot 200}{408.4}

Simplify

sin (x) = \frac{sin ( 13 0 ^{\circ} ) \cdot 200}{408.4}

sin (x) = \frac{sin ( 13 0 ^{\circ} ) \cdot 200}{408.4}

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Take the denominator(s) of

\frac{200}{sin ( x )}

and compare to zero

sin (x) = 0

The following points are undefined

sin (x) = 0

Combine undefined points with solutions:

sin (x) = \frac{sin ( 13 0 ^{\circ} ) \cdot 200}{408.4}

Apply trig inverse properties

sin (x) = \frac{sin ( 13 0 ^{\circ} ) \cdot 200}{408.4}

General solutions for

sin (x) = \frac{sin ( 13 0 ^{\circ} ) 200}{408.4}

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

x = arcsin (\frac{sin ( 13 0 ^{\circ} ) \cdot 200}{408.4}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{sin ( 13 0 ^{\circ} ) \cdot 200}{408.4}) + 36 0^{\circ} n

x = arcsin (\frac{sin ( 13 0 ^{\circ} ) \cdot 200}{408.4}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{sin ( 13 0 ^{\circ} ) \cdot 200}{408.4}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.38455 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.38455 \dots + 36 0^{\circ} n

cot (θ) = - \frac{7}{6}

\frac{2}{π} arccos (m \cdot 1 - 1) = 0

sin (θ) cos (θ) - \frac{1}{2} cos (θ) = 0

cos^{2} (60) + cos^{2} (45) + cos^{2} (x) = 1

3 sin (5 x) = - 1, x < 2 π, 0

What is the general solution for (408.4)/(sin(130))=(200)/(sin(x)) ?
The general solution for (408.4)/(sin(130))=(200)/(sin(x)) is x=0.38455…+360n,x=180-0.38455…+360n