What is the general solution for (182.5)/(sin(36.6))=(248.6)/(sin(x)) ?

The general solution for (182.5)/(sin(36.6))=(248.6)/(sin(x)) is x=0.94786…+360n,x=180-0.94786…+360n

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(182.5)/(sin(36.6))=(248.6)/(sin(x))

\frac{182.5}{sin ( 36. 6 ^{\circ} )} = \frac{248.6}{sin ( x )}

x = 0.94786 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.94786 \dots + 36 0^{\circ} n

Radians

x = 0.94786 \dots + 2 πn, x = π - 0.94786 \dots + 2 πn

Solution steps

\frac{182.5}{sin ( 36. 6 ^{\circ} )} = \frac{248.6}{sin ( x )}

Cross multiply

\frac{182.5}{sin ( 36. 6 ^{\circ} )} = \frac{248.6}{sin ( x )}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

182.5 sin (x) = sin (36. 6^{\circ}) \cdot 248.6

182.5 sin (x) = sin (36. 6^{\circ}) \cdot 248.6

Divide both sides by

182.5

182.5 sin (x) = sin (36. 6^{\circ}) \cdot 248.6

Divide both sides by

182.5

\frac{182.5 sin ( x )}{182.5} = \frac{sin ( 36. 6 ^{\circ} ) \cdot 248.6}{182.5}

Simplify

sin (x) = \frac{sin ( 36. 6 ^{\circ} ) \cdot 248.6}{182.5}

sin (x) = \frac{sin ( 36. 6 ^{\circ} ) \cdot 248.6}{182.5}

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Take the denominator(s) of

\frac{248.6}{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 ( 36. 6 ^{\circ} ) \cdot 248.6}{182.5}

Apply trig inverse properties

sin (x) = \frac{sin ( 36. 6 ^{\circ} ) \cdot 248.6}{182.5}

General solutions for

sin (x) = \frac{sin ( 36. 6 ^{\circ} ) 248.6}{182.5}

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 ( 36. 6 ^{\circ} ) \cdot 248.6}{182.5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{sin ( 36. 6 ^{\circ} ) \cdot 248.6}{182.5}) + 36 0^{\circ} n

x = arcsin (\frac{sin ( 36. 6 ^{\circ} ) \cdot 248.6}{182.5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{sin ( 36. 6 ^{\circ} ) \cdot 248.6}{182.5}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.94786 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.94786 \dots + 36 0^{\circ} n

1 - cos (3 x) = 2 π

(sin (x - 4)) (sin (x - 1)) = 0

θ, r = \frac{10}{3 + 2 cos ( θ )}

sin (x) = \frac{17.75}{42}

tan (θ) - sec (θ) = 3, 0 \leq θ < 2 π

What is the general solution for (182.5)/(sin(36.6))=(248.6)/(sin(x)) ?
The general solution for (182.5)/(sin(36.6))=(248.6)/(sin(x)) is x=0.94786…+360n,x=180-0.94786…+360n