Rearranging terms in Trig equation

  • Thread starter PTX-14
  • Start date
  • #1
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Main Question or Discussion Point

I was reading on planetary motion and have gotten hung up on a "rearrangement of terms" that the author skimmed over. It reads that:

r=e(k+rcos(θ))=(ek)/(1-ecos(θ))

It's been a while since I've been in a math class: I just can't follow how to get from a to b. Is there anyone who can walk me through this like I'm twelve?

Thanks!
 

Answers and Replies

  • #2
551
1
Put all the terms including [itex]r[/itex] on the left hand side and then factor out the [itex]r[/itex]. It might help you to multiply out the brackets on the right hand side first:

\begin{equation}
r = e\left(k + r\cos \theta\right) = ek + er\cos \theta
\end{equation}
 
  • #3
uart
Science Advisor
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Try getting all the "r" terms onto one side of the equation first. That is, try [strike]adding[/strike] subtracting [itex]e\, r\, \cos(\theta)[/itex] to both sides.
 
Last edited:
  • #4
551
1
That is, try adding [itex]r\, e\, \cos(\theta)[/itex] to both sides.
You mean subtracting, surely.
 
  • #5
uart
Science Advisor
2,776
9
You mean subtracting, surely.
Um yeah. Add the negative. ;)

BTW. We both posted at the same time. :)
 
  • #6
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Thank you two, I guess it's time for me to go back and audit some pre-algebra classes... :)
 

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