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# How does sin(0.25) = (r)/(r + 384403)?

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$$Sin 0.25 = {r \over r+384403}$$

That equals 1684.62, but how?

I've been stuck on it for an hour and just cannot figure it out

Guest Jun 20, 2017
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#1
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Sin 0.25 = {r \over r+384403}

$$Sin( 0.25) = {r \over r+384403}\\ ( r+384403)Sin( 0.25) =r\\ rSin( 0.25) +384403Sin( 0.25) =r\\ 384403Sin( 0.25) =r-rSin( 0.25) \\ 384403Sin( 0.25) =r(1-Sin( 0.25)) \\ \frac{384403Sin( 0.25)}{(1-Sin( 0.25)) } =r\\ r=\frac{384403Sin( 0.25)}{(1-Sin( 0.25)) } \\$$

(384403*sin(0.25))/(1-sin(0.25) = approx  126366.362

Melody  Jun 20, 2017
#2
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Note: Melody used "radians" for sin(.25). I used "degrees" to get the same answer that you have:

Solve for r:
0.00436331 = r/(r + 384403)

0.00436331 = r/(r + 384403) is equivalent to r/(r + 384403) = 0.00436331:
r/(r + 384403) = 0.00436331

Multiply both sides by r + 384403:
r = 0.00436331 (r + 384403)

Expand out terms of the right hand side:
r = 0.00436331 r + 1677.27

Subtract 0.00436331 r from both sides:
0.995637 r = 1677.27

Divide both sides by 0.995637: