“Some trees gave their life for this book so that knowledge can be transported into our minds” was a crazy quote!!

@investingpioneer

3 ай бұрын

gave?

@jayloncarter7030

3 ай бұрын

@@investingpioneer were forced to give* sorry

@ryanthomas7119

18 күн бұрын

😂​@@investingpioneer

I'm currently in the final weeks of Precal this semester after relearning everything from the ground up (I had forgotten a ton!) when I decided to go back to school after a 10-year hiatus last September. It's super sad that the class has shrunk dramatically since it started due to most dropping the class. However, thanks to channels like this, Professor Leonard, and Organic Chemistry Tutor I have a 99.63 with only 2 exams left and I for sure got these in the bag. Math is fun and thank you for the motivation as I use your philosophies to keep my head up when I feel overwhelmed with classes. I got Cal 1 in the fall and on my way to finish this Computer Science degree.

@triple_gem_shining

3 ай бұрын

Nice I can relate

@Bylug706

3 ай бұрын

Thats crazy.I just finished College Algebra online from ASU and I signed up for precal and the syllabus is the same as college algebra except with tri added.

@AronMercer14

3 ай бұрын

@@Bylug706 I found a few concepts challenging but once you dive into it it’s definitely doable. I think people were just not doing their homework lol but I know Cal1 is going to be a whole different story so I’m going to do a full course this summer beforehand. I did Professor Leonard’s precal playlist prior to term and it helped tremendously

Mastering the Unit Circle made trig great! Precalc was more about logs, functions, inverse functions, etc. Acing that was easier with the trig, and made Calc II easier. You can do them in either order, but my Algebra II had Trig, just like Algebra I was taught with Geometry. Precalc was more like Trig II. But that was me. ymmv

@AronMercer14

3 ай бұрын

Yep I agree! I think trig is the most fun part of Precal as well as Hyperbolas, etc..

@potato9832

3 ай бұрын

It was a total mystery until I understood the unit circle. It just clicked once I saw the unit circle like a unit square or a polygon normal.

Precalculus is a legitimate subject. Calculus' focus is more on the mathematics (the study of change, motion, and functions) Precalculus' focus is more on the student. (preparing students for the new theories and techniques they will face, learning calculus)

My Precalculus is one semester precalc algebra and one semester precalc trigonometry.

@jakemealey5532

Ай бұрын

Same I’m taking a summer class and we just finished college algebra and started trig today.

I really enjoyed this video! I'm getting ready to start a math degree, so that I can sub in my school district! I'm encouraged when I watch your videos!

Hello, I study architecture. Also one year of electrical engineering in Argentina. I am doing a BIM certificate. I am a designer. The future is computational design. Which math is the base to review to later go into cobol++ , grhaphopper and algorithms. I like math, thus I want to start with the building blocks of the language. I have been following your videos because you are a true teacher and empower people to self discover our potentials! Thank you so much you are a beautiful soul! ❤

Trig is very ... circular and there are infinite series lurking about unseen and menacing , things doesn't resolve nicely like in algebra. regarding pre-calc , Euler wrote the first pre-calc book ! "Introductio in analysin infinitorum"

Before PreCalc it was called "Elementary Analysis" and included the same topics. Check out the book by Kenneth O. May.

My high school combined both Trigonometry and Pre-Calculus into one course and just called it Pre-Calculus. The text book was broad enough to cover all the topics for both. It was a year-long course and IIRC (been a long time,) we basically started off with reviewing the stuff you learn in Algebra I & II, including graphing. Then we covered the main topics in Trigonometry, including definitions, identities and graphing. Then we finished off the course with the Pre-Calculus stuff needed for Calculus, including functions, what a derivative is, some differentiation rules for simple functions, etc. Also, some simple applications of derivatves. And we were introduced to anti-derivatives (Can't remember if simple integration techniques and applications were taught in Pre-Calculus or not in my HS course.) And of course both Trigonometry and Pre-Calculus come in handy when you go head-first into Calculus (along with Analytic Geometry that some Calculus books include.) Funny enough, my HS Calculus course didn't really cover a lot of topics in Analytic Geometry, but my college Calculus did (Analytic Geometry was also offered as a separate course if you wanted a detailed exploration of the subject that Calculus doesn't cover.)

I agree about the trig identity vs algebraic . For a few years I have been trying to self learn calculus and it is a struggle to have any intuitive sense of the trig identity problems

Got a B in precalc. My study habits were very poor and I did myself no favors. Currently in the last 2 weeks of Trig with a 98%. Pretty happy. Only 5 more math classes to go!

From my personal experience Trig was easier. Pre calc was a challenge. I’m currently in calc 1 and struggling 😅. I got an A in trig and B in pre calc. Let’s see what I get in calc 🤔

I took both in college on my way to a Calculus sequence in a B.S. and I found trigonometry to be very rigorous and stressful in requiring tons of memorization of the trig identities and their relationships and towards working long proofs. But it was very satisfying to achieve good grades and help tutor friends in it because of the difficulty. Overall, I felt the grounding received in pre-calc was more immediately useful to completing a calculus sequence in a four year school, where the calculus was a tool in a science degree but not a pure/appied mathematics degree. Calculus I think helps the most to develop the broad mathematical reasoning of defining problems related to general science, that I think pre-calc into calculus is the decent way to go. But taking both trig and pre-calc is the whole package to help develop mathematical reasoning and logic, IMHO.

For me personally, I would say Trigonometry is easier. There's actually a bit of a story as to why... :) There is a game known as Minecraft(I promise this is math related). This game is incredibly flexible in what you can do. That is, you can pretty much do whatever you want and are mostly limited by your imagination. I happened to really like the more technical side of the game, so I would look at the player data, and all sorts of stuff like that. One day however, I remember trying to help somebody out with trying to figure out how to do something. While I can't remember exactly what it was I was trying to solve, it was something along the lines of teleporting r blocks out in the direction I'm facing, or placing a block r blocks out in the direction I'm facing, etc(if you don't know why I picked r, you will see soon :)). Now I already knew what the coordinates of I the player was as that is really easy to get. It was simply some (x, y, z), although I wasn't interested in the z coordinate, so I ignored that. All that was left to do then, was figure out the coordinate of the block that was r blocks in the direction I was facing. If I had that coordinate, then teleporting/placing a block there is trivial. So what I noticed, is that inside the player data, there is some data that gives a list for the direction the player is facing. While I can't remember exactly what it was named, it was something along the lines of x_rot, and y_rot or something like that. Both x_rot and y_rot if I remember correctly, were essentially made up of numbers. So x_rot for instance was a list that had two numbers like [0.52, 0.85...] for instance. What I noticed, is that if I multiply both of these numbers by the distance r, and add each one to their respective x and y coordinates, then that would take me to my desired coordinate. Happy to have figured it out, I shared my result. While I can not remember the exact response I received, I very clearly remember the mention of either "sine", "cosine", or maybe even both. As you can imagine, I was very confused because to my knowledge at that time, I did not use any "sine" or "cosine", just simple geometry, and a few numbers I plucked from some player data. But now I know better... :) This is a simple case of trigonometry in action. For any circle of radius r centered at (a, b), the desired point I wanted to reach was simply (a + rcos(theta), b + rsin(theta)). The "numbers" I was looking at in the past, were simply the calculation of these sin/cos functions(no, I don't mean tan, lol). Most of everything else becomes obvious when you look at a unit circle, realize we are dealing with similar triangles, and multiply all of their lengths by r. So yea, although my memory is a little fuzzy, that is why I would say Trigonometry is easier. It's because I already had a bit of an idea on what it was, before I actually even got to it. Precalculus I kind of had to force myself through, and while Trigonometry was not necessarily easy, it was easier than the alternatives. If I made an error, feel free to let me know and I'll do my best to correct it... :)

I never took Trig before. I want to go back to school for Math, and trig is gonna be a challenge. I loved precalc and algebra.

@solarion33

3 ай бұрын

Check out the Udemy courses by Hania Uscka-Wehlou , she really goes over all the theory patiently and show you proofs from the get go to make you acquainted with mathematical thinking ( rather than just solving a bunch of problems which doesn't really tickle the right parts of your brain for math's) . she has the most comprehensive pre-calc course. along other courses.

@Wandering_Horse

3 ай бұрын

Trig is fun, I say dive in. The trig identities can get a little deep in the weeds but its really interesting to think deeply with them. You will have alot of satisfying 'aha' moments. Have fun!

I did precalculus and trig as part of the same course the last year of HS and both subjects were about the same level of difficulty. I only got a B but I had a good foundation for Calculus in College and got an A. As another commenter said, I think the key to success in trig is mastering the unit circle.

I decided to do 8 week college algebra then 8 week trig in one semester instead of precalc. So glad I went with those two classes instead. My algebra and trig are still weak, but I feel like it's getting better and better each week of calc and physics. Learn that unit circle guys n gals.

Hi Professor. Actually my PreCalc book comprehend Trig too

I have that exact book, plus the solutions work book which is even thicker! I got them in the toss away section at the college library, $1 each! Best $2 deal ever! Yay :)

What are good math learning strategies for audiotorial learners

What is the difference between a precalculus textbook and a book that says algebra and trigonometry? I heard that if you do the algebra and trig you are set for calculus? I am talking about the one form Hornsby on the one hand and Sullivan on the other.

I like precalculus better when it covers ALL of algebra at its advanced level rather than starting with logs and doing the second half of college algebra only. I’ve recently created a sub 7 minute precalculus course covering the full curriculum called Drakes ouTlines

What do you enjoy most about Math? Not sure if my comments are getting through as KZread seems to be deleting them for some strange reason but again I just want to say thanks for getting me more interested in Math. I'm not saying I'll ever be an engineer or Physicist but I do enjoy further expanding my knowledge so I truly appreciate these videos. While I haven't been a student for quite some time you're never too old to learn. I would love to see you review or discuss some Science books as well if at all possible even though your expertise is mainly Mathematics:)

I'm currently taking Trigonometry and Precalculus, and I think graphing Trig functions is very challenging.

In grade 11, we had a choice between trigonometry and functions, which I assume is pre-calculus. I chose trigonometry and was ill prepared for calculus when it came time for the subject.

as an engineer . most of the problems that i solved in math at high school . i found them in real life and in research. and what ive found that most of collegues are not aware of some important concepts in math that the engineering books use and design regulations suggest.

Sir I can't solve this question find the derivative using the chain rule y=e^4-3x can you help me.

@dalitlegreenfuzzyman

3 ай бұрын

I’m assuming you meant e^(4-3x) otherwise no chainrule needed

@eskay1891

3 ай бұрын

Try u = 4 - 3x and solve.

@PhillipRhodes

3 ай бұрын

Did you leave out some parentheses or something? If that's (e^4)-3x then you don't need the chain rule. If it's e^(4-3x) that's different. If it's the latter, remember that the derivative of e to any power is just e to that power. So write e^(4-3x) and then multiply by the derivative of the inside part (4-3x). The derivative of a constant (4) is 0, and the derivative of x is 1, so you get (0-3) which yields -3. So the answer would be -3*(e^(4-3x)).

From my experience trig was easier for me because as you pointed out, it is focused on just one thing and precalc was a bit more difficult for me because it was a wider range of topics.

I never had Pre-calculus. I guess I never needed it in engineering. The best and most used course is trigonometry. The teacher thought it was hard and she thought no one could master it all. She was wrong. I loved the half and double angle formulas. Maybe this is why I later aced surveying. In high school they had a course call Analytic Geometry and in college they made us take it again. Same book. It was a worthless course that I really never used.

as Arabic person when I listen to you and understand you speak English is so Great progress I'm done with most hard part of my journey because I learn it from watching Series & Movies 😂

Pre Calculus by Robert Blitzer. I think Blitzer's Algebra & Trigonometry is the same book, but under the Pre Calculus title, it does have a preview of Calculus at the end. His Algebra & Trigonometry doesn't.

@benhill3098

3 ай бұрын

I have both books, but somehow, I feel more comfortable with Blitzer's Algebra & Trig book, 5th edition. I like the feel of it in my hands as well as the layout and explanations.

There is a lot more memorization with trig than pre-calc. half-angles identities addition rules

@tylermohr25

3 ай бұрын

My precalc covers all that. Probably just depends on the course and its components.

Our society seems to put much more effort into preparing kids for Algebra, which makes Precalc much easier than Trig. If you get lost early on in Trig, I think the penalties are way higher because you can't get away at all with not mastering the basics. But if you get lost early on in Algebra and other aspects of Precalc, most students seem to have an easier time going back to the basics and then catching up as needed.

For me Pre-Cal was no more than a glorified College Algebra course, Trig, on the other hand, was more challenging and exciting.

i thought precalc was harder, but im not sure because i would need see what you were working with compared to my work. i remember teacher telling me, "when you start 1st term in engineering this is where you will start. here with precalc"

@ChristopherBotelho3052

3 ай бұрын

however, i hated algebra and maybe that played a part, im not sure. i mastered and love some parts of algebra but other parts i just struggled with.

@ChristopherBotelho3052

3 ай бұрын

i thought trig was really easy, i always got A in it.

My man

I thought trig was part of precalc?

We never had a pre calc. There was 3 classes of algerbra and 1 trig.

Both require a tremendous amount of practice on my part.

Yeah a lot of trig identities are missing in my mind even though they are useful.

After a few months of doing problems you get used to different ways of problem solving that comes with equations.

Hello from Kurdistan ❤

But trig is part of precalculus

I decided to throw away all my math books. I can't seem to find intellectual friends or anyone that values someone who is intellectual.

@Saudi_Earendel_Atr_

3 ай бұрын

Thats what the internet is good for to find a community you relate too

@Myfavorite192

3 ай бұрын

There are plenty of people who value intellectual conversation and intellectual people, but an interest in math isn’t the end all of intellectual pursuits. I don’t know if this is your case, but I encourage you to find ways to pursue your interests that don’t also belong to your friends while also learning to not look down on others for not sharing those same interests.

@dehiscence

3 ай бұрын

This doesn’t seem like a decision an ‘intellectual’ would make

@noam65

3 ай бұрын

It seems perhaps I'd add two non math books to your reading list, because it sounds like it may be a socializing issue as well. They are called : - how to win friends and influence people - Dale Carnegie - the power of positive thinking - Norman Vincent Peale They are classics. In this day and age, the world is having trouble making physical friends.

@farzamimran3960

3 ай бұрын

I can relate to that a lot but u cant give it up something will happen if u keep going i promise

I have ALWAYS thought Trig should be a one-semester course in high school whereas Pre-calculus was more like a two-semester! Having trig as part of the precalculus course would seem to be the answer! Presently, having the sequence of Algebra 1-Geometry-Algebra 2 is perhaps THE DUMBEST IDEA EVER! Combining Algebra 2 WITH trig is the answer! Of course, having a good teacher is necessary for the student to succeed! My high school math teacher who taught ALL the higher level Math was THE MOST PISS POOR TEACHER I've ever encountered! Getting a Chemical Engineering degree was tough because my math skills were lacking..........but I did! You could also have a solid year combining Geometry with Trig with the Alg1-Alg2 prerequisite. All I know is that presently, nothing is working well and that's a shame!

@ChristopherBotelho3052

3 ай бұрын

i feel the same as you, and i thought precalc was way harder, they gave us algebra 1, 2 and 3 before we got trig, once i got into trig i fell inlove with it, untill we started precalc, thats when i felt lost.

@argonwheatbelly637

3 ай бұрын

I had Algebra/Geometry, then Algebra II/Trig. Precalc was more of cleaning up concepts of functions and tying some expanded concepts from the prior ones, e.g. Complex numbers, etc. But this was in the late-70s/early-80s.

@solidpixel

3 ай бұрын

precalculus and trig in the same course is how we had it in my HS. Our sequence was Algebra I, Algebra II, Geometry, Then precalculus with trig

@Mcdude22

3 ай бұрын

When I was in highschool it went algebra 1, geometry, algebra 2, then pre-calculus/trig combo. These days I think they blend it all together, though, with algebra and geometry being taught together over the course of 2 or 3 classes, called “integrated math”, then steps into trig/pre-calculus combo