Rearranging terms in Trig equation

In summary, the conversation discussed a rearrangement of terms in the equation for planetary motion. The author was struggling to understand the process and asked for clarification. Two individuals provided guidance, suggesting adding or subtracting terms in order to simplify the equation. The author expressed gratitude and mentioned needing to review pre-algebra concepts.
  • #1
PTX-14
2
0
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!
 
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  • #2
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
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
uart said:
That is, try adding [itex]r\, e\, \cos(\theta)[/itex] to both sides.

You mean subtracting, surely.
 
  • #5
Nylex said:
You mean subtracting, surely.
Um yeah. Add the negative. ;)

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

What is the purpose of rearranging terms in a trigonometric equation?

The purpose of rearranging terms in a trigonometric equation is to isolate the variable being solved for and make the equation easier to solve. This can also help in identifying patterns or relationships between the terms.

What are the steps involved in rearranging terms in a trigonometric equation?

The steps involved in rearranging terms in a trigonometric equation include identifying the variable being solved for, moving all terms containing that variable to one side of the equation, and simplifying each side of the equation by using trigonometric identities and properties.

Can all trigonometric equations be rearranged?

No, not all trigonometric equations can be rearranged. Some equations may be too complex or involve multiple variables, making it difficult to isolate a single variable and rearrange the terms.

What are some common trigonometric identities used in rearranging equations?

Some common trigonometric identities used in rearranging equations include the Pythagorean identities, sum and difference identities, double angle identities, and half angle identities. These identities can help in simplifying and transforming trigonometric expressions.

Are there any tips for rearranging terms in trigonometric equations?

Yes, some tips for rearranging terms in trigonometric equations include carefully writing out each step, using proper notation and symbols, and checking your work by substituting the rearranged equation back into the original equation. It is also helpful to practice solving different types of trigonometric equations to become more familiar with the process.

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