Sunday, October 22, 2006

3.4 Derivatives of Trigonometric Functions

Hey guys. Let's expand our growing knowldge about derivatives, shall we?

So basically, 3.4, the class favorite, is about finding the derivatives of trigonometric functions (you know...like sine, cosine, tangent...all that fun stuff).To start off, let's use y=sin(x) and find the derivative by graphing.

f(x)=sin(x):


And now...after marking the zeros and the slopes at the right points...f(x)=sin(x) and its derivative (in red):
Wow..doesn't the derivative of the sin(x) graph look oddly like the graph of f(x)=cos(x)?? Well it is! So thus:Now, let's do the same thing to the f(x)=cos(x) graph in order to find the its derivative.

f(x)=cos(x): After making the derivative graph (in red), you get this: Incredible. It looks to me that the derivative of the cosine graph is:
Knowing the derivatives of sine and cosine, the you can find the derivative of tangent. How? look below.
The derivatives for the inverse trig functions are as followed:
Sample Problem as follows: Okay SOPHIE you are up next!

4 Comments:

At 8:18 PM, Blogger princessophie said...

I love lesson 3.4!!!!!!!!!!!
it uses all the fun identities we learned last year. the class we had for this section was so enthused....making us all major nerds and i think i have come to terms with that fact and i will accept it.

alison with one l: i have not yet used anyone else's notes, or even really read them for that matter, however i checked this weekend to see if your blog had gone up yet because i was really excited to see it (and once again, the major nerd is coming out of me). it was not up the first time i checked, but it is now and i have read the whole thing and immensely enjoyed it. thank you

 
At 5:54 PM, Blogger lauren said...

HEY! ok I really like all of your graphics because they came out really well. I also thought that you did a great job covering the section!!! THANKS FOR THE HARD WORK!

 
At 1:32 PM, Blogger Genevieve said...

Could someone help me with when we need to find where y=0. I am confused because we have to use math from last year, which, frankly, left my head after the final.

 
At 1:36 PM, Blogger Lisa said...

Allison you are brilliant. Thanks for including the graphs of all the logarithmic functions. They really helped me grasp the concept. And i love the comic!

-lisa

 

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