ap calc comic
Storyboard Text
- Our story begins at an average American high school where two seniors are struggling in their AP Calculus Class. This week, their topic is trigonometry derivatives and they are LOST!!!
- AP CALC EXAM 2022
- I don't know how we're ever going to memorize these trig derivatives, they're so confusing!!
- OMG!! i know what to do! We can go to a study session with Ms. Littlelog!! She can help us memorize the trig derivatives and do great on our AP Calc exam!!
- I know!! I tried making a quizlet, flashcards, everything!! I just can't seem to make any progress. What should we do?!?!
- Haha! You two are pathetic!! It's just some trig derivatives, whats so hard? How are you going to do well if you don't know something so easy?
- Be quiet!! We're going to put our best work in and get this stuff down!!
- Jenna's right!! With the help of Ms. Littlelog, we can both memorize these derivatives, do a bunch of questions with them, and get a 5 on the exam!!
- We'll see, only a few students have ever defeated me and they all knew the trig derivatives by heart.
- What are you doing here you pesky ghost? Haven't I warned you to stay away from my students?!
- Oh Ms. Littlelog, do I have news for you! Jenna and Darcy here don't even know their trig derivatives! How do you expect them to gets 5s now?
- I have faith in my students, they're smart and they work hard! With a few extra lessons, they'll be masters of trig derivatives. Girls, come with me!!
- We're sorry Ms. Littlelog, but that scary ghost was right! We're clueless when it comes to trig derivatives.
- This is so cool, I can't believe it!! But, how are you going to help us?
- I'm going to give you some great tips for memorization and then we're gonna do some practice problems together. By the end of this period, you two will be trig derivative prodigies!!
- Girls, I have a surprise for you! My name is Calculadora and I'm a master of calculus. I travel from school to school with the disguise of Ms. Littlelog, helping AP Calc students. Today, I'm here to help you with trig derivatives!!
- Ok, we're ready. Lay it on us, Calculadora!!
- Let's start with the two most basic trig values; sinx and cosx!! Sinx and cosx are probably the easiest because they are almost reversible opposites of each other. See, d/dx sinx is cosx and d/dx cosx is -sinx!!
- There are 6 trig derivatives that you must know by heart to succeed! Memorizing them and knowing how to plug them in to the appropriate equations guarantees you a 5 on the exam!!
- Wow, I never though of it like that. Now, I'll always remember that I can switch to and add a negative sign for cosx and I'll have my derivatives. What about the rest?
- "PSST"SEXC - SECX -TANXCSCX - CSCX - COTX
- Ok, let's go. Now, we have tanx, cscx, secx, and cotx. Here's a hand tool for memorizing these trig derivatives, just remember the phrase "PSST"! This may make no sense now but look here.
- Memorizing this word and chart will allow you to memorize your trig derivatives with ease! With this chart memorized, all you have to do is follow the arrows and you'll get your answer. For example, let's say you need to find d/dx of secx, find the secx that's not in the middle and see what the arrows point to. You'll see that for secx, thr arrows point to secx and tanx, which is perfect because d/dx secx is secxtanx! This works for every value! Look again, find cotx on the chart and see where the arrows point. They point to -cscx and cscx, which is amazing because d/dx cotx is -csc^2x. These are the basic steps you need to take to defeat the AP Calc Exam and get a 5!
- "PSST"SEXC - SECX -TANXCSCX - CSCX - COTX
- Wow! Thank you so much, Calculadora. Darcy and I are ready for this test!!
- "PSST"SEXC - SECX -TANXCSCX - CSCX - COTX
- No problem! Good luck girls!!
- They are not ready because I always win!! But let's get started. What is the derivative of secx?
- Okay, Jenna and Darcy, are you ready to face the Ghost of the AP Calc Exam?
- A FEW MONTHS LATER
- sec x - sec x - tan x
- Oh I remember this! The derivative of sec x is secxtanx because the arrow rom the sec x thats not in the middle points to secxtanx!!
- sec x - sec x - tan x
- That's correct. How about the derivative of tan x?
- That's so easy, Ghost!! It's sec^2x
- Well, that's correct too. I bet you can't answer this question. What is the derivative of cscxcotx?
- This is hard!!
- You got this
- Jenna was able to defeat the Ghost of AM Exam's hardest question and the girls got a perfect score!!
- Well, if I use the quotient rule, f'(x)= u'v - v'u over v^2. cscxcotx = (-cscx + cotx)(cotx) + (-csc^2x)(cscx)= -cscx cot^2x + (-csc^3x)= -cscx cot^2x - csc^3x
- Congrats girls, you have beat the Ghost of the AP Calc Exam and have received 5s!!!
- You can see that the derivative section of the AP Calc Exam can be solved by remembering the rules given to you by Calculadora!!
- We did it!!
- Good job!!
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