Calculus 2 Lecture 6.5: Calculus of Inverse Trigonometric Functions

Calculus 2 Lecture 6.5: Calculus of Inverse Trigonometric Functions

[huiyichen]

I used to excel in math, but because of some tough times I had to pull myself out of school for 2 years to work. I forgot everything I knew about math and having to take calc 2 without any refresher, I thought I was completely hopeless. The professor I have just dived right into calc 2 as if all the students took calc 1 with him. Well I didn't. Not being able to understand anything that was written on the board, I wanted to cry. But here you are, an angel disguised as a math professor. All hopes are not lost. :) Thank you.

[darthboganis]

Requirements for a function to have an inverse 0:00
> Trig functions generally aren't 1:1. But restricting the domain allows us to treat them as inverse functions
y = sin (x) 4:00
> What does the inverse do? 5:30
y = cos (x) 10:20
y= tan (x) 14:15
y = csc (x) 17:00
y = sec (x) 22:50
y = cot (x) 27:30
w/ Examples 30:00
Compound trig functions 38:00
Properties 46:00
Inappropriate Domain issue 50:00
Derivatives of Inverse trig functions 52:30
Proofs 56:00 cosine inverse [implicit just means chain rule]
> using an identity 58:30 [cosine y]
> using triangles 1:01:00 [secant y]
w/ Examples 1:07:30
Harder problem 1:10:30
Even harder problem 1:16:00
Harder still 1:22:15
Sidebar: using triangles solve cos-1 (x^2) 1:26:00
> 'some fancy maths' 1:30:05
Integrals of inverse trig functions 1:32:20
w/ Examples 1:35:30
Third example rewriting the function into the right form 1:43:00
> In this example the function was rewrite in the 1/1+u^2 form so that it could be integrated using the tables. Important to consider algebraic manipulation, substitution etc... look for patterns.
Last example 1:47:00 [using substitution twice]

[SilverArro]

I can't believe I just watched 2 hours worth of Calculus lecture in my spare time. It's truly a testament to how inspiring you are as a professor. Thanks for all the hard work you've put in to making these videos! :D

[MrCompenso]

If you could do videos on physics, I think my life would be complete.

[Maladringe]

His videos should be more popular, this guy really knows how to teach his stuff. I wish my college professor was as good as him :(

[honeyraj]

You know he is a great teacher when I'm here studying watching his videos, 8 years after he posted this.

[chicknkin]

Your a gift from god. My Calc 2 teacher is a fool without these videos I would 100% be failing.

[tenzinkunsang]

Professor Leonard teaches math "as Raphael painted pictures, Michelangelo carved marble, Beethoven composed music, or as Shakespeare wrote poetry." In short, thank you for being one of the best educator!

[mr.jceniza]

I understand you a lot better than my professor. I come to his class and take some notes, but ultimately, right after class, It's with you that I learned! THANKS A LOT! Not just an inspiration and a role model mentally, but physically as well! Who in earth could have a nice physique while teaching math? hahhaha

[Pompadour]

skip to 51:39 for the calculus part and you already know the basic trig

[TheCrushenator]

I wanted to state what a fantastic professor you are. My current professor seems to gloss over topics without ever going over edge cases or techniques to use for solving more difficult problems. You have saved me from a very difficult situation. These lessons are excellent! Very clear, and we'll explained

[MrMegaHamSandwich]

I'm going to show this to my grandchildren one day.

[Cam._S]

Derivatives start at 1:07:28
Integrals start at 1:32:17

[marieb.]

I have a calc 2 exam tomorrow. I barely did any hw because the wow xpac release. I realized this morning that I am a fool as I sat down to "study." Now, after finding this video I feel there still may be hope. And yes, I think I have learned my lesson.

[sandlertossone]

I totally love your simplicity as a teacher. The inverse trig intergration method is way better than the a and u method where you have to memorize two separate formulas for each. Thanks

[Jono.]

Covered the exact same content that I had in my first class except this time my head didn't explode. I'll be using your videos all semester and I hope you know what a great service you are doing for everyone!

[sskylark_]

This video is 5 years old today, and I would just like to say that I am thankful for your work. Your videos are crucial to my math education in college. Thank you Professor!

[sozngcs]

I have to say thank you so much you really have helped me so much with eng maths.. honestly can't say it enough thank you. Your teaching style is amazing.

[cssfriendly]

You are the greatest teacher i ever had till now. Your classes are even better than those of Khan Academy!! You are the true saviour of The CalculusVerse.

[Ireemo]

keep on uploading videos ur a superman disguised as a math teacher