Tuesday, January 19, 2010

Derivatives of Other Trigonometric Functions (Scribe Post for Monday's Class)

Welcome to a snowy day in Carbondale, Colorado. Today's topic of interest: The derivatives of trigonometric functions.

In the beginning of class, we reviewed a few topics from trigonometry including the reciprocal properties, the quotient properties and the Pythagorean Properties. Here are the slides from the notes we took in class. It also includes the derivations of the four other trig functions. Hope it helps!

I found the unit circle diagram for the Pythagorean Properties very helpful, but in case this is hard to read, here is a summary of the three types of properties:




Ok, so now onto the fun part, the derivatives of the other trig functions. In order to discover these derivatives, we used the quotient rule.
(Just in case you forgot, the quotient rule is the derivative of numerator times the denominator minus the numerator times the derivative of the denominator all divided by the denominator squared.)

So here are our the results of our derivations for the six trigonometric functions:

In order for this to be true though, x must be in radians

Here are some of the memory aids we came up with in class:
- Derivatives of "co" functions have negative signs
-from Pythagorean Properties
+tanx goes with secx
+cotx goes with cscx
+sinx goes with cosx

Here is a short video I found helpful. It has a few examples:
3.5 Derivatives Of Trig Functions
View more presentations from ricmac25.


If you have any questions at all please feel free to leave a comment.

And the next scribe is..... drum roll please.... Beston

Here is the sample derivation for secant:


  1. These scribe posts keep getting better and better. I'm so impressed. Not sure I'm looking forward to when it is my turn and I have all of ya'll's to compare to!

    I love the variety of this post. Lots of color (fun to read), plus, I think that finding animations, like the slide show you found, make for great learning materials. I sometimes have a hard time finding enough examples from the book or class for myself to fully understand the topics. I have used a few different outside sources like this that have been a huge help. Awesome job!

  2. Hey, so yeah- ditto what skirdude said. I really found that reading this post was the perfect combination between being in class and reading the book. The way this is formatted is very clear and the colors are really helpful in organizing everything. What proved to be the most helpful for me in this post were the memory aids. They were a great help, I look forward to making a scribe post as detailed as yours!

  3. Heya,

    This post is gorgeous. Really well laid out and logical and oooo.

    A couple thoughts to consider:

    I have a memory device for the quotient rule that I didn't post on the quotient rule scribe post, because I didn't want to steal the thunder of the guy singing that weird song. But here it is:

    If your equation is f(x)/g(x) then you call f(x) high because it is on the top, and g(x) low, because it is on the bottom. Then the quotient rule is:

    "low d high less high d low, draw the line and down below, denominator squared will go"

    (you just say d like the letter d - so for instance d high means derivative of the top)

    I still sing this softly under my breath when doing the quotient rule.

    Final thought: any chance you'd consider adding a sample derivation to your post? Just in case someone doesn't want to click through to the slides from the class? Just to give us a taste?

  4. Thank you all for your comments. I'm glad my Scribe Post helped you understand the derivatives of trig functions better. Kwad, thank you for the memory device for the quotient rule. It really helped me visualize it a bit more.

    I will include a sample derivation from class for secant. I am not exactly positive how to post an equation from the equation editor into a comment, so I will add it to the end of my scribe post. Hope that isn't too inconvenient.

  5. This post was phenomenal, i really glad to see everyone taking such a high level of interest and putting such a great deal of effort into every scribe post. However i would really like to see some examples, maybe the ones from the homework and possibly a few more from another sources.

    Here is a few examples from the awesome UC Daivs site i found and have grown to love.


  6. This post was awesome. The colors in this post were a bit much. They were a bit distracting in places like in the explanation of the quotient. The samples at the end of the post are going to help me during tomorrows quiz. Some more example would be great. The examples in the video helped somewhat. Good post over all Blue elephants

  7. This was a very good scribe post. I liked your use of colors, but I do agree with J-tron that were distracting, but only in few spots. Overall this was a well organized post. I liked the second slide show, it had good examples, and was a good visual aid for remembering these derivatives. This scribe post was a helpful tool for me in studying and remembering today's lesson.

  8. This post was very good. I liked how first you reviewed the properties we learned in precalc. I also liked how you talked about how we used the quotient rule to find the trig rules and reviewed what the quotient rule was. One thing I might suggest is that you post how we got each of the trig rules by using the quotient rule. Because they were rety simple proofs, people can probably get them on their own, but it might be helpful for anyone who may have missed class to see each step for how we got from sec'(x)=tan(x)*sec(x)and the rest because I know when I first started on that exploration I was very unclear on even where to start.

  9. Thanks for adding the derivation, its totally fine to add to your post.

    It helps to show some derivation, because I don't know the methods you guys use in class. When you say derivation it could mean you go all the way back to first principles, or you do something funky, I don't know. So it really helps an outside reader to give a little taste of what you do in class!