## 17Calculus Article - You Can Take Good Notes

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This page contains suggestions on how to take good notes or links to articles that we think will help you. First we discuss how to take notes that make sense. Then we mention a specific technique, called flow-based note-taking.

How To Take Notes That Make Sense

Taking good notes is critical to learning and making class attendance worth your time. It is very frustrating to be studying for an exam and not be able to decipher notes taken in class. So how do you take good notes?

First, you need to prepare for class by reading the material that the instructor is going to cover. Now wait! I know what you are thinking. All instructors say to read the material before going to class and most students don't do it. Either we run out of time or we are barely able to get things done as it is. Reading seems like such a waste of time. Well, let me tell you, it's not a waste of time and here's why.

Anytime you hear something the first time, you will miss a lot. You will probably hear only about 20-25% of what the instructor says. Then you probably will write down only about half or less of what you hear. However, if you read the material before class, you can increase significantly the amount of material that your brain can process and you can take better notes. Also, you will what to write down and what not to write down. You literally can't write down every single thing the instructor says and writes. But if you have already read the material, you will know what the instructor is adding and what they are taking straight from the book.

Now, reading the material before class doesn't mean that you have to understand it and, most likely, you won't understand hardly anything. However, your brain will start processing it as the instructor is speaking and you will be surprised how much you WILL understand during class.

In class, it is important to take notes by hand, not by typing. There is some scientific evidence to suggest that taking notes by hand helps you remember information longer. Here is an article that may help you understand why. [Take Notes by Hand to Remember Information for a Longer Time] Now, taking notes by hand doesn't mean it has to be done using a pencil and paper. You can use an iPad or a laptop with a writable screen. As long as you are writing notes by hand, that is the key.

Here is a trick that grad students use to comprehend new material. Once you have the notes from class, go back home and rewrite the notes as soon as you can. Here are the critical things to do while rewriting.

 Make sure you do it the same day as the class asap, before going to bed. Rewrite them while filling in holes in logic, concepts and words you left out. Use your best handwriting and good grammar. Make the thoughts complete. Get your notes to flow smoothly through the material. Supplement your notes with sentences, thoughts, ideas, definitions and theorems from your textbook. Structure them to make sense to you.

If you do these things, you will end up knowing the material and being better prepared for exams.

We also have some suggestions for taking good notes when you do not plan to keep your textbook on the books page.

Flow-Based Note-Taking

Taking good notes that you can use to effectively study is critical to your success as a student. However, most students are never taught how to take good notes. Most of the time we just copy down what the instructor writes on the board and try to write down as much as we can of what he/she says. But is this really the best way to learn?

One of our favorite blogs about learning by Scott H. Young, has an article about a way to take effective notes that really help you learn the material. The technique is called Flow-Based Notetaking and it can revolutionize your classroom experience by making the time you spend in class worth it.

The idea is to learn while you are actually in class taking the notes, not only later when you are alone trying to decipher cryptic notes that seemed to make sense when you wrote them down. Using his technique, your notes flow from one concept or idea to the next and make sense.

You CAN Ace Calculus

### Trig Formulas

The Unit Circle

The Unit Circle [wikipedia] Basic Trig Identities

Set 1 - basic identities

$$\displaystyle{ \tan(t) = \frac{\sin(t)}{\cos(t)} }$$

$$\displaystyle{ \cot(t) = \frac{\cos(t)}{\sin(t)} }$$

$$\displaystyle{ \sec(t) = \frac{1}{\cos(t)} }$$

$$\displaystyle{ \csc(t) = \frac{1}{\sin(t)} }$$

Set 2 - squared identities

$$\sin^2t + \cos^2t = 1$$

$$1 + \tan^2t = \sec^2t$$

$$1 + \cot^2t = \csc^2t$$

Set 3 - double-angle formulas

$$\sin(2t) = 2\sin(t)\cos(t)$$

$$\displaystyle{ \cos(2t) = \cos^2(t) - \sin^2(t) }$$

Set 4 - half-angle formulas

$$\displaystyle{ \sin^2(t) = \frac{1-\cos(2t)}{2} }$$

$$\displaystyle{ \cos^2(t) = \frac{1+\cos(2t)}{2} }$$

Trig Derivatives

 $$\displaystyle{ \frac{d[\sin(t)]}{dt} = \cos(t) }$$ $$\displaystyle{ \frac{d[\cos(t)]}{dt} = -\sin(t) }$$ $$\displaystyle{ \frac{d[\tan(t)]}{dt} = \sec^2(t) }$$ $$\displaystyle{ \frac{d[\cot(t)]}{dt} = -\csc^2(t) }$$ $$\displaystyle{ \frac{d[\sec(t)]}{dt} = \sec(t)\tan(t) }$$ $$\displaystyle{ \frac{d[\csc(t)]}{dt} = -\csc(t)\cot(t) }$$

Inverse Trig Derivatives

 $$\displaystyle{ \frac{d[\arcsin(t)]}{dt} = \frac{1}{\sqrt{1-t^2}} }$$ $$\displaystyle{ \frac{d[\arccos(t)]}{dt} = -\frac{1}{\sqrt{1-t^2}} }$$ $$\displaystyle{ \frac{d[\arctan(t)]}{dt} = \frac{1}{1+t^2} }$$ $$\displaystyle{ \frac{d[\arccot(t)]}{dt} = -\frac{1}{1+t^2} }$$ $$\displaystyle{ \frac{d[\arcsec(t)]}{dt} = \frac{1}{\abs{t}\sqrt{t^2 -1}} }$$ $$\displaystyle{ \frac{d[\arccsc(t)]}{dt} = -\frac{1}{\abs{t}\sqrt{t^2 -1}} }$$

Trig Integrals

 $$\int{\sin(x)~dx} = -\cos(x)+C$$ $$\int{\cos(x)~dx} = \sin(x)+C$$ $$\int{\tan(x)~dx} = -\ln\abs{\cos(x)}+C$$ $$\int{\cot(x)~dx} = \ln\abs{\sin(x)}+C$$ $$\int{\sec(x)~dx} =$$ $$\ln\abs{\sec(x)+\tan(x)}+C$$ $$\int{\csc(x)~dx} =$$ $$-\ln\abs{\csc(x)+\cot(x)}+C$$

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