Friday, October 26, 2012 - Deriv of Trig Inverses and more!!

Scribe post!

Friday October 26^th, 2012

We started class by going over the last quiz, #3. O’B said that he was very proud and everyone did a great job! YAY! 

Quiz problems:

#1.) Very nicely done everyone!

#2.) Matching functions with derivatives. O’B said that this will again be on the quiz on Tuesday. Practice these problems by playing that fun game with the confetti! Remember  to not only pay attention to maximum and minimums but also to where the function is increasing and where it is decreasing. 

#3.) Good job on this one, just remember to not let the thetas throw you off. Use the quotient rule because there is no way to reduce the fraction.

#5.) Remember that velocity is the derivative of position and acceleration is derivative of velocity. Also, that speed is absolute value of instantaneous rate of change not average rate of change. 

#6.) O’B encouraged us to keep memorizing those trig derivatives! 

#7.) Just rise over run. 

#8.) This one is just straight up chain rule. 

BONUS: The trick for solving the bonus is that you have to use the product rule! It is a combination of product and chain rules, but use product rule first. O’B warned that on the next quiz it will not be a bonus, but just a regular question. 

O’B then went over some things that we should be memorizing. 

AKA how to spend your time in the shower:

• Trig values - practice with quizlet!
• Trig derivatives - all six! 
• Quotient rule!
• Product rule!
• Chain rule!
• Power rule
• Definition of derivative as:
• H --> 0
• X--> c forms
• UPDATE: Know the following bullet points too!!
• Logax
• a^x
• 6 Inverse trig

Memorize and be relatively articulate for the test on Monday! 

We then did a quick little outline of what is going to happen in the next couple of weeks in AP calc. 

Remember that there is a quiz on Tuesday and finely crafted test on the following Monday!

O’B reminded us that he is going to be gone from Friday until Wednesday but will still be able to answer any questions through email or better yet, the questions google document. However, if you do ask a question while he is away, be sure to include the problem because he will not be bringing his textbook.

- - - - - 

We then conducted a finely crafted exponential and logarithmic investigation:

Our goal was to get inverse trig derivatives but first we started by remembering our inverses for trig functions.

http://mathworld.wolfram.com/InverseTrigonometricFunctions.html

Wolfram does it again. Helpful information about graphs, domains and ranges, and calculator inputs available in the link above. 

We then reviewed that helpful identity that states that

Wait for more

Identity

Inverse sin + inverse cos - pi/2

Same for sec and csc

Tan and cot

PG 175 #5  -- UPDATE: 

Gotta use a chain rule!

Derivatives for Trig inverses!! 

UPDATE:

How did we get those though?

O'B went over an example of how to find the derivative of a trig inverse using Cosine. 

Memorize the derivatives for inverse sin, tan, and sec when needed and then remember that the others are just the negatives of the first three!