How To Remember Circumference & Area – 2 Fun Mnemonics

Hello and welcome to Algebra Demystified! Today I’d like to tell you about a great mnemonic tool to remember the formulas of the area and circumference of a circle. As you know, I love mnemonics, and whenever I find a good one, I’m always posting it on my blog!

I’ll start by listing the two formulas and the legend of the symbols (what the letters mean in the formulas). Then I’ll tell you the (short) mnemonic phrases. I meant to build the suspense up to the end, but you may skip to the end if you’d like and work backwards.

C = πd

The legend goes as follows:

1. C stands for the circumference,
2. d stands for the diameter of the circle.

The diameter of a circle is the length of a line that you can draw between two points on the edge of a circle, provided you cross the center. You would do it like so:

And the formula for the area of a circle is:

A = πr2

The legend is:

1. A is the area of the circle,
2. r is the radius of the circle.

The radius is the distance from the center to any of the points on the edge. If you’d like a neater explanation, just take any of the halves of the diameter formed by the center. Both of those halves could be called a “radius”.

Now comes the mnemonic:

Cherry pies are delicious! Apple pies are too!

I left the most fun part for the end! Those two mnemonics stand for the two formulas I mentioned in this post. It’s better to remember them together, since they form a great logical blend.

Cherry (C) pies (π) are delicious (d)!

Apple (A) pies (π) are (r) too (²)!

There’s only one caveat to this mnemonic, which is not to mistake the “are” in the first sentence with a “r” in the formula. But remember, we never put radius and diameter together in any formula, since the radius and diameter of any circle can be expressed in terms of each other. In other words, if you know the radius, you can calculate the diameter by doubling the radius. And if you know the diameter, calculating the radius is no big deal: you simply divide by 2.

As always, suggestions, thanks, or just any comments are welcomed in the Comments section! Thanks and I hope that my blog post has helped you in some way! 🙂

How to Remember the Quadratic Formula

Hello! Sorry for the long break from my last blog posts, it was really something I shouldn’t have allowed myself given the relative success of my last few blog posts. Anyway, I’ve decided to break the ice here with a quick mnemonic tool concerning the quadratic formula.

This formula lets you solve quadratic equations, which by some are considered to be one of the difficult aspects of algebra. Some consider it to be a gibberish concatenation of as, bs and cs along with some coefficients. Yet it is crucial to the very existence of algebra and its related subroutines.

Here I take a picture of this formula:

 

And here’s a mnemonic to help you remember it. It comes in various modifications if you ask different people, but the basic version goes about like so:

A negative boy was undecided whether or not he should go to a radical party but his 2 friends who were boys went and there they met 4 amazing chicks and stayed up until 2am.

Let’s examine the various parts of this “story”:

1. A negative boy – (-b)
2. Was undecided – (+-)
3. … to a radical party – (square root symbol)
4. his 2 friends (b^2)
5. … 4 amazing chicks – (4ac)
6. stayed up until 2am – (division by 2a).

Hope this helped and stay tuned for more!

Remembering Trig Identities: An Elegant Mnemonic

Hello! Today I’ll tell you of an elegant mnemonic to remember the main trigonometric identities. You may have heard of it, but it’s not widespread at all.

First, let’s make sure we’re on the same wavelength. There are 6 main trigonometric functions – sine, cosine, tangent, secant, cosecant, cotangent. They represent various ratios of various sides of a right triangle. If you don’t understand what they stand for, I can’t explain it now, it’s beyond the scope of this blog post; but you can look them up in Wikipedia right here.

It turns out that certain trigonometric ratios are related to other ratios in very interesting ways. Many students have a hard time remembering them (me too!) Only recently have I found out that there is a very elegant way to represent all the major trig identities concisely, and I’ll share this technique with you now.

It’s called “the hexagon” of trigonometric identities. Since there are 6 trig functions, it just makes sense to use a hexagon, right? 🙂

On the edges of the hexagon you can see the trig functions, in the center – you can see the number “1”. The key to this hexagon is that you don’t need to remember the trig identities, only the structure of the hexagon. It’s relatively easy to recreate the hexagon, or you may keep a draft of it and carry it with you at all times. So, that said, let’s begin exploring!

The product of any two opposing edges of the hexagon equals 1. So, we get:

sin(x) * csc(x) = 1
cos(x) * sec(x) = 1
tan(x) * cot(x) = 1

That shouldn’t be very hard to remember. Just multiply two opposing edges, and you’ll get 1 as a result. Now, for the next portion:

The two top vertices of any inner triangle (initially squared), when added, give the bottom vertex (squared).

sin2 x + cos2 x = 1
1 + cot2 x = csc2 x
tan2 x + 1 = sec2 x

These are what we call the “standard” identities. They might be a bit confusing, but they aren’t. Just take the top two vertices (or corners) of an inner triangle, square them, and add them. As a result, you’ll get the bottom vertex of the inner triangle, also squared. It takes some practice to get these results quickly, but you’ll get the hang of it pretty soon. 🙂

A trigonometric function on the hexagon equals the product of the two adjacent trigonometric functions.

tan(x) = sin(x) * sec(x)
sin(x) = cos(x) * tan(x)
cos(x) = sin(x) * cot(x)
cot(x) = cos(x) * csc(x)
csc(x) = cot(x) * sec(x)
sec(x) = csc(x) * tan(x)

This one should have been a bit easier than the last one. You just take any trig function. It equals the product of the two adjacent trig functions (on both sides of the initial function).

This whole hexagon thing may seem difficult at first, but actually, we derived 12 (!) trig identities from it! I’m sure it will help you a lot, especially if you’re in high school. Trigonometry is really an important topic, and these trigonometric identities play a crucial role in your success in this subject.

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