Tuesday, February 9, 2010

Derivative of Inverse Trig Functions

Calculus… Episode 2/9/10: The Scribe Post Strikes Back.

Monday we discussed the topic of Derivatives of Inverse Trigonometric Functions
Let’s begin. We started out with a quick refresher on the different trigonometric functions and their individual inverse. Since none of the trig functions pass the horizontal line test because they are periodic, none of them are actually invertible functions or one-to-one functions. So in actuality they are inverse trig relations. Therefore in order to actually create an inverse of the functions you must restrict the domain of each so that they do become one-to-one functions.
This is simply done by taking only half of their corresponding unit circles.

This chart shows all of the inverse trig functions and their derivatives. Illustrating how they are to be used is shown above in those few example equations from class. Below I provided a few links that hopefully will be helpful. Lastly the next scribe post is dammitimmad.



  1. love the title!! it would be great if you could title the graphs, and maybe post them in an order that shows their relations. Also i saw a couple of graph repeats. If there is a way to get a clearer picture for the equations that would be very helpful for any of us that missed class.
    Otherwise nice job with all the uploading!

  2. It is interesting that restricting the unit circle to either the top or right half covers all the functions or relations... Why aren't/can't they be bottom or left side? Does it matter if its the opposite side of the circle since they produce the same values only negative?

  3. nice job! This was an accurate and easy to understand account of class on monday. Like Tubby said, it would be helpful to label/comment on the picture of the graphs you posted so that people could understand what they mean. I like how short and to the point it was and didn't drag on with unnecessary words.

  4. This looks good. Looks like you put a lot of time into this. This was a hard topic to scribe about and be creative with because we really only learned about the graphs. However you did put all the same graphs that we learned about in class and were on the slides from class. I think you could have just linked to the slide show and that would have saved you a little work.

  5. Great job on posting different types of graph on the scribe post. This topic was hard to demonstrate just by writing several paragraphs. you did great job. However, as other people mentioned, it would be better to add titles of the graphs and explanations of it. Also better quality of screen shot will make your scribe post look nicer.

  6. HI Winn Plot,
    A lot pictures in your post, great illustrations, I like it. I realized that the graphs for function of sin and inverse sin are same graphs. That’s a small error appearing in your post. Otherwise, your post is pretty good.
    However, one thing I really want to point out is that it is a little bit different to find the derivative of inverse of tan and sec. So It would be better if you can provide us the illustration for that, too.
    Overall, great job.

  7. Over all this is a very well done scribe post. There is almost an excess of pictures. But, all of the pictures you used were necessary seeing as we were reviewing trigonometric graphs and their inverses. I agree with skirdude's suggestion of placing a link to the slides in your scribe post to save you time and effort. But hey, nobody ever complained about someone else's hard work that benefits everyone. If you were to add on a title or explanation to each of the individual graphs you have here, I would have suggested that it would be better for the post to contain all of the pictures of the graphs. This would have made for a very long post though. Because you didn't (which is perfectly fine, because most prefer a less verbose post which I give you kudos for) it may have indeed saved time to have put in the link to the day's slides. If you felt like doing something a little easier, with a little more pizazz. Perhaps you could have added a link into your post that explained the graphs and the inverses instead if you didn't feel like doing quite so much screen capturing. Here is a link you might consider adding or just looking at http://www.5min.com/Video/Derivatives-of-Inverse-Trigonometric-Functions-164055118 . It might make you appreciate Bru a little, no I take that back, a lot more. If you actually take the time to watch any of it at all you will know what I mean. Excuse me now while I go wipe the brown dirt off my nose.

    Good Job Winn Plot.

  8. Hey Winn Plot!
    I appreciate the time that you had to have put into this scribe post. Uploading all those graphs is definitely time consuming, but it was also necessary for the day's lesson. I liked your title, it was creative and brought me a smile. A couple things: there were two y=sinx graphs, instead of sinx and sin'x. That was the only error. I noticed your links at the bottom, they were helpful sources, but I'd recommend pointing them out, or adding them as hyperlinks. While your formatting was a little crazy at times, it's understandable because the graphs can mess that up. I thought your scribe post was informative and did a good job summing up the day's lesson, and the links you provided were helpful as well
    Thanks Winn Plot!

  9. Winn Plot,
    Great job on your scribe post. I am a visual learner and really like how you included all of the graphs and derivatives. My only suggestion might be to put your text under the graphs as opposed to on the side and maybe putting the trig functions and their inverses next to each other. Other than that awesome job and thanks for a great scribe post!

  10. This was a quality post, I understood everyting that you put on it. I did think that you could have either writen a little bit about each of the graphs as others have mentioned, or just linked to the slideshow. All of the graphs overwhelmed me a little bit when I was reading it, and an explination would have been nice. As somebody also mentioned the screen shots could have been a little bit better quality, as it was I had a hard time reading some of them. To make this post less conviluted I might have used more words (and when I used them not have them off to the side of the post like that, I was a little confused...), I had to figure some of the stuff out myself. Figuring it out myself might actually have helped me understand it better, so that could be a good strategy. Thanks for a great post.

  11. Hey Winn Plot, great post.
    You clearly put a lot of effort into the images and I clearly understood what happened in monday's class. I think that the formatting could have been a little cleaner in terms of mixing pictures and text. Also, I did not quite understand the last sentence on your first image. Maybe you could have spent some time explaining each image and I think you could have put the definitions image before the example image. Other than that, great, thorough job

  12. Nice post I really like all the graphs, it makes the subject really clear. A few of them are a little hard to read but that's the computers fault not yours!! I found this really good slideshow that explains this subject in terms of the actual math instead of graphs, it seems like the website it's on is a little like what we are doing with all this blog and wiki business, online learning!

    Here's the link to the slideshow:

  13. Yo Winn Plot, I honestly did not understand most of this post. Like Tubby said the graphs could use more explanation, and the post in general could use more explaining. I should be able to see what we did in class and I get the general aspect of what we went over but overall I am not too sure what it all means. Some of the graphs are hard to read and I understand that it is the computers fault but that wouldn't happen if you wrote directly on the scribe post. I also got the link but it would be helpful if instead of telling us where to go, if you just told us the info that was there. Sorry for bashing but I was not satisfied.

  14. Winn Plot, I really like your first description, for me it provides a very direct approach to the subject. The detailed way that you describe the way in which inverse trig relations and functions worked for me. I have not read all the above comments but I think that I got the gist that some people found it hard to read, I would suggest formatting. If you space out your paragraph and add some color and maybe some words in italics and bold it makes it much more interesting to read. I think that you did a great job with having lots of images too, maybe just again, format it.

    Thanks for the post,


  15. Hey,

    Since we only use the top half of the unit circle for inverse functions, they don't actually look like the ones in your pictures, right? It might be helpful to show at least one example that restricts the inverse to the top half of the unit circle so we can see what that looks like? That's always been a confusing thing to me - why do we have to restrict it, since we can figure out what it would look like, and also, who would ever want to take the inverse of a trig function anyway? Gross.