I have a HORRIBLE memory. I cannot memorize a formula to save my
life. Yet, I am majoring in mathematics. I?m assuming you already
know the sin= opposite/ hypotenuse type of rules and are looking for
ways to memorize things like sin(x)^2+cos(x)^2=1. If you are looking
for the first type of rule I suggest the age-old SOHCAHTOA rule:
http://www.pen.k12.va.us/Div/Winchester/jhhs/math/facts/sohcahto.html.
There are three ways to avoid having to force yourself to memorize formulii.
The first (and my weapon of choice) is getting a good graphing
calculator! The newer ones TI comes out with are capable of ?symbolic
manipulation? (e.g. you say sin(x)/cos(x)*tan(x) and it says
tan(x)^2). In my opinion math is about being able to solve problems,
not to stuff easily forgotten rules in your head to pass tests. If
you become calculator-literate you will be better suited to solving
real-life problems in your future than those who were trained by their
teachers not to use technology.
In the very likely case that you aren?t allowed to use calculators to
solve these problems (I should write a book on why teachers should
never that do that) most of the trig rules stem from fairly simple
algebra. If you?re strong at that you may be able to derive the
formulas you need. By definition sin=opposite/hypotenuse, cos =
adjacent/hypotenuse and tan = opposite/adjacent. Using algebra you
can see that:
sin/cos = (o/h)/(a/h) = o/a = tan
If you replace every instance of sin with o/h, cos with a/h and tan
with o/a you should be able to solve many of these problems without
memorization. If you stick to this method I?m sure you?ll eventually
pick up the rules...its sometimes easier to remember something once
you understand the mechanics behind it. Once again, this approach
will place you above those who simply remember the rules without
knowing the math behind it. There are cases such as
sin(r)^2+cos(r)^2=1 that algebra alone cant solve...for these you just
need to remember the functions as used in a unit circle sin(r) is the
y value, cos(r) is the x value. According to Pythagoras
A^2+B^2=C^2...by the same logic (noting that on a unit circle C=1)
sin^2+cos^2 = 1^2 = 1. There?s almost always a way to figure these
rules out...you just have to be sneaky sometimes.
My third idea is nothing new...but its sometimes the only way:
practice. Don?t practice the rules per se, no flash cards needed.
Practice in context, try to do a problem set from your textbook or
online and keep track of how many you get right. If you?re in a jam
you can always try using the algebraic approach above. You will most
likely notice improvement after the first three or four times you go
over it. If you need practice problems I?m sure you can ask a
teacher, they always have out-dated textbooks lying around.
I hope this helps.
-Fractl |
