Remembering Trig Functions

Date: 09/27/2001 at 20:50:40
From: Kim 
Subject: Remembering trig functions

Hi! 

First of all, thanks for taking the time to read this. 

We are required to memorize the sine, cosine, tangent, secant, 
cosecant, and cotangent for 30, 45, and 60 degrees for precalculus 
class. I've made flashcards, but it's still pretty difficult. Do you 
have any tips on how to remember these? 

-Kim-

Date: 09/27/2001 at 21:04:58
From: Doctor Peterson
Subject: Re: Remembering trig functions

Hi, Kim.

People have different ways to remember; you may have to think about 
what sorts of things you remember most easily, and why, and then 
design a plan for memorization that fits your style. I can only tell 
you what fits my own style.

I like pictures and patterns; I learn connected facts better than 
isolated facts. So I first remember these relations among the trig 
functions:

        +             +             +
       /|            /|            /|
     1/ |sin     sec/ |tan     csc/ |1
     /x |          /x |          /x |
    +---+         +---+         +---+
     cos            1            cot

(Actually, I remember the first of these and the definitions of the 
other functions in terms of the sine and cosine in order to 
reconstruct the other two.)

Then I remember two special triangles:

            +             +
   sqrt(2)/ |            /|
        /   |1        2 / |sqrt(3)
      /45   |          /60|
    +-------+         +---+
        1               1

You can figure these out for youself using the Pythagorean theorem if 
you need to, or just memorize the numbers on the pictures.

Now you can just read off the function values from the pictures. For 
example, the sine of 60 degrees is the ratio of the "opposite" side 
(vertical) to the hypotenuse, from my first picture; in the 60-degree 
triangle, this is sqrt(3)/2. Those ratios that I use often I will just 
know; but when I have trouble, I go back to these pictures in my mind 
to recall a ratio.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/