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/
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