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### Remembering Trig Functions

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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/
```
Associated Topics:
High School Trigonometry

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