Talk:Basic Trigonometric Functions

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Response to checklist

The general structure of the page looks good. The biggest issue is adding numerical examples to help explain your definitions. See the notes below for more detail. AnnaP

References and Footnotes

  • All images are credited
  • No direct quotes or specific references used

Good writing

Quality of prose

  • The first paragraph doesn't clearly define the topic, but I think that the first section as a whole defines the topic and that the TOC provides all the outlining necessary.
  • Each section is clearly relevant.
  • Several sections build towards a thesis instead of starting with one, but I think that it reads better and is less confusing that way. In the Unit Circle section, for example, I can't think of any way to give a meaningful statement of purpose up top, because if you don't know what the Unit Circle is, the thesis won't make sense to you.

After you say "That is,  \overline{AC} divided by  \overline{AB} is the same  \overline{AE} divided by  \overline{AD} ." , can you actually write that out in equation form? That will help readers who are more visual thinkers and make the previous sentence less confusing.

Kate 14:17, 24 June 2011 (UTC): Done.

This sentence: "Trigonometric functions are the functions that connect an angle with its associated ratios." isn't going to make sense to readers who aren't already very comfortable with ratios (that's more people than you'd think). I'd suggest finding a different way to say this, or even turning it around and saying that ratios can define an angle or that we use trigonometric functions to define the relationship between a particular ratio and an angle. Regardless, I think that there needs to be a little bit more before moving on to the next section.

Kate 14:17, 24 June 2011 (UTC): I'm afraid you're going to have to elaborate more on this comment. I've added a definition bubble for ratio, but I don't see how saying "We use trigonometric functions to define the relationship between a particular ratio and an angle" is significantly different than saying "Trigonometric functions are the functions that connect an angle with its associated values". To me, it seems like a matter of wording. And what do you mean by there needs to be a "little bit more" here? What kind of "more"?
I've re-read it, and I think a large part of the problem is the repetition of the word function adding to the word ratio. A page of this level will be most useful to high school students, and I can tell you that all of my experience with high school students indicates function is a difficult word. Students typically become comfortable with the word during either algebra 2 or precalculus (that doesn't mean that haven't seen it earlier, but there's a difference between seeing and being comfortable with it). Students at that level likely won't need this page. Does that make sense?
Long story short, I think the goal should be to only use the word function once in any sentence, particularly those that involve the word ratio. I'm now actually thinking that a helper page for function could be helpful, but that's besides the point.
Kate 19:24, 24 June 2011 (UTC): Ohhh, ok! That makes much more sense now. You're right, I remember that "function" didn't make perfect sense until Algebra II, while this page is definitely directed at kids who are in Geometry. I'll try and re-work it using those words less.

This idea: "These new definitions give us a way to think about trig functions for angles that are greater than 90 ° (or π/2 radians). When we were thinking of sine and cosine in terms of right triangles, we had no way to define their values for angles greater than or equal to 90° because we couldn't draw a right triangle with that as one of the non-right angles." is really critical, but it's buried in your page in a way that it won't strike the reader as particularly important. Try to find a way to move this to the beginning of the section.

Kate 14:17, 24 June 2011 (UTC): Rephrased this paragraph and moved it to the top of the section.
Awesome. It flows much better now and provides the reader with the motivation to go through that complicated section

Integration of Images

  • Images are all labeled, and the text links to and describes the purpose of the images.

Figures 5-7 should be bigger, because it's hard to see all of your labeling on them as is (notably, the alpha in figure 6 is difficult to see).

When I'm looking at the page (the browser takes up most of my 13 inch screen), your paragraph about figure 5 is down by figure 6, which is a bit confusing. Similarly, your description of figure 6 is down by figure 7.

Kate 14:43, 24 June 2011 (UTC): Made the pictures bigger and moved them around. I think it's a little uglier now, but things are closer to where they're talked about and hopefully easier to read.

Links to other pages

  • All the pages linking to Basic Trig are in the mouseover bubble at the top
  • Most of them aren't linked to in the body of the page, but I think that's as it should be - you need to know what "sine" means to understand the Law of Sines, but you don't necessarily need or want to read about the Law of Sines just because you've read about sine.

Examples, calculations, proofs

  • Math-language definitions and calculations are provided for each new idea

This is the biggest area where I'd like to see improvement. I'd like to see an example when you introduce sine, cosine, and tangent, right off the bat, as well as in other places where you introduce new topics. Using numerical examples will greatly help the reader understand what's going on.

You may even want to go back to your figure 1 and add some numbers and use that to build examples. Another key place for an example is to go with this sentence: "The input of a trig function is the output of an inverse trig function, and the output of a trig function is the input of an inverse trig function."

Kate 14:48, 24 June 2011 (UTC):
  • What do you mean by numerical examples of sine, cosine, and tangent? Just pictures of triangle where it's like, look, there's a 30° angle and when we divide these two sides we get 1/2?
Yes, I mean having a triangle with the sides labeled (with numbers) and actually showing what the ratios are (and doing any necessary division).
  • I am opposed to the idea of adding numbers to figure 1, as the point of that picture is that the ratios are the same regardless of the size of the particular triangles. Adding numbers would tie it down to statements about one or two triangles with one specific angle in the corner, whereas I'm trying to make statements about any right triangles.
Okay, then I'd suggest creating a second image to use for the purpose of examples. The numerical examples are necessary, but they won't make sense without a picture.
Kate 20:53, 24 June 2011 (UTC): Added in another picture and numerical examples throughout the Specific Functions section.
  • The inverse trig section is actually Harrison's, I'll point your comment out to him when he gets back.
I'd actually like to see Harrison's explanation simply bump you back up to Kate's explanation, rather than have the mouseover. That should be doable by adding in an anchor. 6/30 AnnaP
Kate 18:08, 30 June 2011 (UTC): anchor & link added; although of course the link only works when the unit circle section is expanded.

Mathematical accuracy and precision

  • All statements are accurate, to our knowledge. Mistakes pointed out by others have been fixed.
  • Effort has been made to make statements as precise as possible without being confusing or overwhelming.
  • Mouseovers with definitions have been used, and the point of the page itself is to define a whole bunch of terms.

The mouse over for "reference angle" is unclear. Adding an image here could be really helpful.

Kate 14:49, 24 June 2011 (UTC): There are so many pictures in this section, so I tried to explain it better with words outside of a bubble instead of adding yet another picture.
That works better, aside from your "&theta" that didn't turn itself into a  \theta .
Kate 19:50, 24 June 2011 (UTC): aaah I didn't even see that! fixed!
Kate 20:04, 24 June 2011 (UTC): Also, I just re-did the paragraph dealing with reference angle and the caption to the picture with all the reference angles, hopefully they explain things better now?
Your use of beta is confusing. Is there any reason why you can't just use theta? AnnaP 6/30
Kate 18:09, 30 June 2011 (UTC): changed it.
Going back through this page, the fact that you (both) switch between using "trigonometric functions" and "trig functions" is a bit off putting. Can a sentence be added earlier on to clarify that these terms mean the same thing? AnnaP 6/30
Kate 18:09, 30 June 2011 (UTC): Added a sentence about this up top.


  • Effort has been made to keep paragraphs short. Many images are used.
  • Hide/shows and mouseovers have been used where appropriate
  • We have viewed the page in several different window sizes on several computers, and we feel that the current layout reflects the best balance between sometimes having awkward white space and sometimes having isthmuses of text squeezed between images on either side.
  • There isn't any weird preview text

General Comments

* Rebecca 12:31, 31 May 2011 (UTC) You should check out the page on a smaller window if you haven't already. Figure 5 is pretty far away from the paragraph were you explain it. If you've already tried to address this, don't worry too much about it- it's not too bad as it is.

Great aspects of the page:

  • Your writing is very clear! Keep it up.
  • Nice use of spaces to keep the page readable.
  • You might want to consider making the headings of the sections "sine" etc. under the "specific functions" heading smaller (the same size as "secant" etc. would probably be good). The section will be easier to read that way.

I can't wait to see your intro section/ main image and the why it's interesting section. This is great so far, and I'm sure you'll be able to find some good applications. Good luck!


Dayo 1:26 6/27:I put in an alternate definition for an inverse trig function that could help clarify its' uses and purposes.

Co-authoring discussions between Harrison & Kate

I moved the pictures in the Unit Circle section around. They all line up, which I know we don't really like, but having them on opposite sides made the text much more difficult to read when the window was narrow. What do you think? -Kate 20:35, 24 May 2011 (UTC)

I moved things around & tried it with a variety of window sizes. It's still not beautiful, and I'm not a huge fan of the two pictures being on top of each other, but I think this is the best balance between isthmuses of text and oceans of white space. Also changed the wording on the arctan part a little - used period instead of iteration because I thought it was more accurate, added in a bubble to explain period. Check that you agree with the definition in my bubble. -Kate 14:25, 24 May 2011 (UTC)

Ahhh Harrison, I'm sorry, I broke your table!! I thought it was complicated enough that it should go in the hidden section, and I swear I only copy and pasted it, but now there's only a "{" showing up! :( -Kate 17:40, 23 May 2011 (UTC)

Harrison, I agree with most of your edits (especially the way you described creating the right triangle in the circle), but I was trying to keep it friendly and informal on purpose, so I might put back some of the "we"s and "our"s. I really see the purpose of this page as being a more casual introduction to trig than one would find in a textbook or classroom, and I think the conversational language makes it more comfortable to read for people with less math background. We can talk more about this on Monday, if you like. -Kate 01:55, 21 May 2011 (UTC)

switched the order back to x=cos theta, y=sin theta -- since the problem is framed as "let's solve for x and y", I think it looks better if x and y are on the left.
You added in the sentence "Note, however, that this side is treated as though it were a negative distance for the purposes of evaluating trigonometric functions.", which is true, but I think it gets adequately addressed later.
Removed the "feel free to" before the link to the cool app. It seemed… flippant(?) to me
-Kate 02:10, 21 May 2011 (UTC)


It would be prefect for the unit circle section. It even showed my why tangent is called tangent!

Harrison Htasoff 20:40, 20 May 2011 (UTC)

Woah, that's awesome! I wonder if it's uncopyrighted, and if so, if we can steal it! If not, is it permissible to link to it?? -Kate 22:18, 20 May 2011 (UTC)

It isn't an applet, so we'd have to link to the page, which is markedly different than ours. I cant seem to download the file either. We could try putting it in as a good site to refer to. Htasoff 00:40, 21 May 2011 (UTC)

Section-specific comments



  • It might be good to have one picture that shows lines that are perpendicular to the horizontal line and another picture that shows lines that are perpendicular to the diagonal line.
  • I think instead of "intuitively," you mean "visually."

Thank you, Becky! Those are all very good suggestions.
-Kate 13:04, 20 May 2011 (UTC)
All of these things are fixed.
-Kate 22:19, 20 May 2011 (UTC)

  • xd 20:09, 12 June 2011 (UTC) maybe you want to mention that \overline{AB} means the line SEGMENT joining point A and point B just in case read is wondering what that overline is.
Kate 13:37, 13 June 2011 (UTC): I had originally written "line segment  \overline{AB}" for that reason, but Prof. Maurer didn't like that because it's actually redundant, but now that you mention it I think I'll try and put a balloon in to explain.xd 20:32, 13 June 2011 (UTC) cool

Specific Functions

The Unit Circle

  • I would change "We can connect our right-triangle based definitions of trig functions from above to the Unit Circle by dropping a line from any point on the circle, down to the x-axis. Thus..."
"Our right-triangle based definitions of trig functions from above can be related to the Unit Circle by dropping a line from any point on the circle down to the x-axis. By doing such, we create..."
because using "connect" to mean relate here is a little confusing.Agree about connect vs relate, changed it in my own words. -Kate 18:55, 23 May 2011 (UTC)
  • In the next line, I would change the sentence to "Whose horizontal leg is defined by the x coordinate and vertical leg is defined by the y coordinate" instead of "whose legs each have a length of either the point's x or y coordinates." Agree, changed. -Kate 18:55, 23 May 2011 (UTC)
  • Before, we found the measure of an angle using our knowledge of the side lengths of a triangle. Now, we will use our knowledge of the measure of an angle to find the side lengths of the triangle. I disagree - we weren't finding the measure of an angle before, we were defining / learning about what sine is. -Kate 18:55, 23 May 2011 (UTC)
  • You need to emphasize more that you've solved the question of the side lengths for the case where the triangle is in the unit circle, and now you want to solve the case where the radius of our circle is not 1. You can use the same equations, but you should resolve to show that x= rcosθ etc. Put in another set of equations -Kate 18:55, 23 May 2011 (UTC)
  • Did someone suggest that you give all your angles in radians as well? I think you should stick to degrees, and if you really want to discuss radians, to do that in a different section.We wanted to make some connection to radians, because they're helpful for the inverse functions and Harrison's written another helper page about them. I agree that giving both each time is unnecessary, but I've kept the first link. -Kate 18:55, 23 May 2011 (UTC)
  • Great use of mouseover for supplementary angle.
  • I would move figure 7 down and put tons of spaces between the paragraphs. The page looks nice the way it is, but it's hard to tell which picture you should be looking at first. Spacing isn't ideal - I spaced it out on one of the super-widescreen computers. Will try and move things around to make them better. -Kate 18:55, 23 May 2011 (UTC)


Thank you for the comments, Becky! -Kate 18:55, 23 May 2011 (UTC)

Inverse Trig Functions

I think what's there is good. I think it'd be worthwhile to also talk about:

  • Graphing, and how restricting the domain is necessary for the inverses to pass the vertical line test CHECK I like the way that was done. -Kate 21:54, 23 May 2011 (UTC)
  • Why tangent-1 and cotangent-1 can take all real numbers CHECK
  • The differences between all the various types of notation- arcsin vs. sin-1 vs Sin-1 CHECK
  • Some sort of problem-solving context

-Kate 20:44, 23 May 2011 (UTC)

xd 01:21, 25 May 2011 (UTC) just one little thing. you might want to mention the concept of "mapping" and illustrate it with two real number axis. For example, sine maps real numbers between negative inf to positive inf (domain), to real numbers between -1 and 1 (range), etc. And inverse operation is to find the number in the domain that corresponds to the number between -1 and 1 (the range). You know what I mean.