Talk:Law of cosines

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Contents

Response to Checklist

For this page, I'm following the Checklist for writing helper pages. This is a page that is somewhere between a helper page and an image page I think. There are helper pages written to assist with this page, yet this page is there to ultimately provide some help for the Solving Triangles page.

I agree that this is somewhere in between a helper page and an image page. I think it works as is, though, overall. (You'll find my responses to your page in red throughout this section) AnnaP

Message to Future

  • This page links to the Solving Triangles page, which more thoroughly describes the applications of triangles and such.
  • There may be some other topics linked to the law of cosines (LOC) like Heron's formula. Topics like this, however, would make more sense here if there was more talk about perimeter and area.

References and Footnotes

  • Not much in this department. All of the images are credited to me in the references section, where the programs I used are also listed.

Quality of prose and page structuring

  • This page is very to the point and concise. What needs to be on the page is on the page, and it is set up to mirror the layout of the Law of Sines page.
  • The only thing that I can think of as possibly being superfluous is one of the two proofs. Because I'm talking about the LOC as a generalization of Pythag Thm, it makes sense to use that proof, but the distance formula proof is one of the most common ones. That's why both are justified to be there.
  • I placed the simpler proof first.

Can you provide some motivation as to why we'd want to approach a proof using the distance formula before diving right into that proof? You could even say something to the effect of "for a second proof." It's a little bit awkward to just jump right in

Done-zo. Richard 6/23

Integration of Images and Text

  • The images on this page are placed intentionally so that they can be used as references for the proofs and examples.

Links to other pages

  • So far, so good here. This links to all of the triangle pages. Hopefully there will soon be a Pythag Thm page soon to link to.

Examples, Calculations, Applications, Proofs

  • I think that one of this page's strengths is the math part of it. The proofs and example problem really explicitly and simply show the LOC.
  • The basic description includes when exactly the LOC is useful in solving triangles.

Mathematical Accuracy and precision of language

  • This page spells everything out in the proofs and the example with the mathematical formulas, and explains anything that may be confusing.

I agree, but you've got an extra  b^2 hanging around in your proof using the distance formula. I think you had a copy/paste problem :)

Thanks, Anna!!!!! Richard 6/23

Layout

  • The paragraphs are pretty short, the layout is pretty good and not unappealing. I adjusted the screen size to check for funky margins and this page looks pretty safe.


  • The one concern I may have with this page is the main image, but I played around with it and there's little to do to make it both interesting and not weird. For now, I think this works for sure.

General Comments

Rebecca 17:07, 9 June 2011 (UTC)

  • Great page! Well explained I think...
  • Have you considered trying a why it's interesting section? Even just to quickly list some things it might be used for? You could also provide a link over to your shadows page in a why it's interesting section.

Any Suggestions?

Basic Description

Kate 15:51, 9 June 2011 (UTC):

  • This section isn't very interesting, but I think it does the job of explaining without getting to complicated. My one concern is that I don't see a link to the Basic Trig page anywhere, and I think this is the part of the page where such a link should go.

  • Read over your last paragraph in this section (the one that starts "The law of cosines is useful"), some of the sentences don't fit well together or are internally awkward.

Rebecca 16:53, 9 June 2011 (UTC)

  • I would change "trigonometric extension" to "generalization" in the first part. I think it's less intimidating.
  • I think the basic description should be reorganized a bit. Your first sentence is good, but then I would move the rest of that paragraph to a later part. I'd put the part beginning with "Given a triangle..." and the equation and the next paragraph right after that first sentence. Then, after you've explained the equation for the law of cosines, it seems logical to discuss how it's similar to the Pythagorean theorem.

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Alternate forms

  • Particularly when the law of cosines is being used to find a particular side length, that is when a certain angle measure is given, the law of cosines can be written in several different ways to help set up the equation to solve for the missing element of the triangle.
I think this would read better as:
The law of cosines can be written in several different ways to help set up the equation to solve for the a specific missing element of the triangle. This is particularly helpful when it is being used to find a certain side length.

Rebecca 16:53, 9 June 2011 (UTC)

  • Kate is right- I think you wen't "particularly" crazy in this section. ( PUN :D )

  • typo: This for isolates the term

A More Mathematical Explanation

Rebecca 17:05, 9 June 2011 (UTC)

  • We've found that people get intimidated by saying things like "An easy way to think about..." because if they don't understand immediately, they feel like they should just give up.

Proof

Kate 15:51, 9 June 2011 (UTC):

  • The explanations within the proofs are really good.
  • Rebecca 17:05, 9 June 2011 (UTC) Agreed. Very clear
  • One thing: you should explain where the coordinates for A come from in the second proof.

xd 20:46, 13 June 2011 (UTC) I think you should explain what x_1, x_2, y_1 and y_2 mean in  \text{distance} = \sqrt {(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}}

Example Problem

  • I think these are a really good idea, and I think this one was explained well.

Rebecca 17:05, 9 June 2011 (UTC)

  • I would consider including a hide show right after the problem that says "hint" in the link. The hint could be something like "Use the law of cosines to find side lenght C first."
  • I would also write out the law of cosines again so that people can see that you're just subsituting values. This might be kind of obvious... i don't know. Just a thought.
  • Instead of "simplifying for" before you have the equation c^2 = 36 + 72 - 72 I would say "simplifying the last term".

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