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:
#1: THE RECIPROCAL PROPERTIES:
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#2: THE QUOTIENT PROPERTIES:
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#3: THE PYTHAGOREAN PROPERTIES:
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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:
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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.
http://www.slideshare.net/share/blogspot/116892
REMEMBER TOMORROW IS VIRTUAL WEDNESDAY. YOU CAN CHOSE WHETHER TO COME TO CLASS OR TO DEVELOP YOUR OWN VIRTUAL LESSON. The topic is: the derivative of inverse functions.
http://www.slideshare.net/share/blogspot/116892
REMEMBER TOMORROW IS VIRTUAL WEDNESDAY. YOU CAN CHOSE WHETHER TO COME TO CLASS OR TO DEVELOP YOUR OWN VIRTUAL LESSON. The topic is: the derivative of inverse functions.
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:
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