Pre calculus college level memory tricks!?

Question

does anyone know any helpful pre calculus (university engineering level) tricks/hints or memory tricks? for example today I learned SohCahToa which stands for Sine = opp/hyp Cosine = adj/hyp Tangent = opp/adj.

any type of trick or hint or catchy memory tip that any of you know and would like to pass on would be appreciated.

Answer 1

Is there something specific you want/need to memorize? Precalculus is a vast area of math and it encompasses many different things.

Answer 2

To be honest with you Yes - I had alot of them - but that was 30 years ago - and I've forgottem them all, as well as what they were supposed to mean.

I wished I had learned it right in the first place! If I had learned them for real and them forgotten then I may even be able to recall some of them, and be able to answer some of these questions without first doing a calculus, or geometry/log search to search the rules first!

My advice - just learn them. But a set of flash cards and write the problems on one side and answers on the other side. In between classes, instead of picking up chicks - sit under a tree and go through the cards a few times - after a while you'll know them and you won't need the tricks.

Sorry for the "realistic" advice. (ask you self this - would you want your Dentist remembering a trick answer about how to do a root canal?).

Answer 3

I just finished taking pre-calc last semester so I know your pain. SohCahToa is the most important one but the only other mnemonic that I know of is All Saps Take Calculus (ASTC). ASTC is used to show in which quadrant sine, cosine, and tangent are either positive or negative. The letter denotes what is positive. A is in Quadrant I and A means all three variables are positive. S is in Quadrant II and it means sine is positive while cosine and tangent are not. T is in Quadrant III and means tangent is positive while the others aren't. Finally, C is in Quadrant IV and it means cosine is positive while the other two aren't. Hope it helps!

Answer 4

Learn the unit circle:
They say some professors make you memorize it. Mine didn't but I tried anyway and it paid off at exam time. It is just one part of learning trig facts but it is daunting until you break it down. In fact, I only learned the top half by heart and it still saved me during exams to know it. It's not much more effort to learn the bottom half as well.
When you are doing other work, stop now and then to draw the circle. Repeat as often as you can until you can whip off the drawing in a matter of seconds with all the information. Just break it down into steps as you learn it.
The circle has its center on the origin of the x/y axes. The radius of the circle is 1 (just remember it's a unit circle) So label where the circle's circumference cuts the axes at the 4 points: (1,0), (0,1), (-1,0) and (0,-1). You should know which points these are just by looking at the axes. (-1,0) is going to be at the negative end of the x axis, for example.
The circle is not divided up in equal pieces. Starting with 0 degrees on the (1,0) point, travel up the circle, counter-clockwise. Always travel counter-clockwise - traveling clockwise has consequences you will learn about if you haven't already.
The degree stops along the way up will be 30,45 and 60. Practice writing those points on the circle (you don't have to measure, just approximate). Once you are used to that, memorize pi/6, pi/4, pi,3. These are the equivalent radian degrees of 30, 45 and 60. You can figure each out by calculating the degrees times pi/180 but if you know them already, you don't have to do that.
For each of the degrees mentioned: 30,45, and 60, next to each write the (cosine,sine) values. They are respectively (the square root of 3 over 2, 1/2), (the square root of 2 over 2, the square root of 2 over 2), and (1/2, the square root of 3 over 2).
Knowing those three sets of values, the order in which they appear, starting with the first point at 30 degrees - that will get your started on quickly learning the entire circle.
Quickly write in the degrees that are at the (1,0), (0,1), (-1,0) and (0,-1) spots on the circumference. They are 0 degrees, 90 degrees (as you would expect since the axes are perpendicular to each other), 180, 270, and finally, 360- which also is the 0 degrees starting point. 360 degrees because you have made a full rotation.
Now fix in your mind that 360 degrees is 2 pi. You can work it out but it is such a useful fact anyway that you'll be using it a lot.
Once you know that 360 is 2 pi, then you know that the halfway point which is at the other end of the x-axis is 180 degrees and that is half of 360 or 1 pi. The 90 degree point is half-way to 180 so it is 1/2 pi or pi over 2. The 270 degree point at the bottom of the circle is 1 and a half pi or 3 pi over 2. It is a pi and a half. 180 degrees and a half of that (180+90=270).
Without too much agony, you can learn all of this so far and practice drawing the circle with just that information to start.
Then number the quadrants which you already know how to do from graphing. They are upper right: I, upper left: II, lower left: III, lower right: IV.
Number them quickly and add underneath the numerals, respectively, (++), (-,+), (-,-), (+,-) If you want to also put A,S,T,C around the quadrants, in that order, then you are utilizing another trick mentioned here.
You can do these things pretty quickly and it helps to take a half minute to automatically generate all this information on a piece of scratch paper during an exam.
I said that the first spots on the circle (exclude the whole number coordinates at the four axis points when memorizing this stuff) were pi/6, pi/4 and pi/3. Skip over the 90 degree point at the top of the circle and work your way down the other side of the circle, traveling down. Stopping at another set of 30 and 45 and 60 degree points (added to 90 degrees, they are 120, 135 and 150), you just need to memorize 2pi/3, 3pi/4 and 5pi/6. Notice that the denominators match those of the radian degrees on the other side. The first (cosine,sine) value - which is for 120 degrees - is exactly the same as the one directly across from it in the first quadrant. They face each other across the y axis and the only difference is that 120 degrees (2pi/3 radians) has (-1/2, square root of 3 over 2). You know that is going to be the case if you look at the (-,+) you wrote under the quadrant number.
I could go on and on. There are only going to be pairs of (cosine,sine) values with radicals in them that you are going to see and the form a pattern, lying directly across from each other and repeating just when you cross the x axis.
I explained all this to show just that it looks daunting but broken down into steps, it is easy. Of course you have to practice. Other people have charts that they use to show all the values and patterns. It takes really about half a minute to put the circle on paper and load it up with information that is not so hard to learn. As I said, I only learned the top half perfectly. The bottom is easy too - the only thing I didn't memorize for it were the radian degrees. Not too bad since they are easy to calculate.

Answer 5

Sir, I send a rhyme excelling
In sacred truth and rigid spelling
Numerical sprites elucidate
For me the lexicon's full weight

Now you know the first 20 digits of pi (add the letters of each word). Sure it's cute, but it probably won't help with your class. Sorry.

Answer 6

Here is one:
“All Students Take Calculus”
ASTC (Where are they positive?)

Which trig functions are positive in each quadrant:

All in Quadrant I,

Sine in Quadrant II,

Tangent in Quadrant III,

Cosine in Quadrant IV.

Answer 7

I guess your pre-calc class includes trigonometry. Here's another one I remember. Note the pattern in the 3rd column.

sin 0 = cos 90 = sqrt(0)/2
sin 30 = cos 60 = sqrt(1)/2
sin 45 = cos 45 = sqrt(2)/2
sin 60 = cos 30 = sqrt(3)/2
sin 90 = cos 0 = sqrt(4)/2

Answer 8

I know this is goofy, but you know that song Oh Ay Oh Ay! Oh Ay Oh Ay! (I don't know the name of it, but it's the intro to an 80's song. It's kinda got a Caribbean beat.)

That's how I remember it. First I write

o
--

a
--

o
--
a

Then I just put the 2 h's

o
--
h

a
--
h

o
--
a

Answer 9

I was taught to remember by saying...

Saddle Our Horses

Canter Away Happily

To Other Adventures

Answer 10

oscar
had
a
heaq
of
apples

sin= o/h cos=a/h tan = o/a