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Self taught trig

by Krazie
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Krazie
#1
Sep23-04, 06:19 PM
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Would it be possible to buy a trig text book and read it straight through and teach myself? Do people do this? I know that it is very hard to teach yourself calculus, but isn't trig much easier to teach yourself?
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Tom McCurdy
#2
Sep23-04, 06:23 PM
P: 1,113
SOH
CAH
TOA

there I taught you trig
lol, jk

I do believe it is possible to teach yourself trig, although like with anything it will take practice and dedication

However the basic applications of trig should be very easy to pick up-- of course in hindsight i guess most things seems easy once you know them

If you have any questions about trig just ask and I will see what i can do
Krazie
#3
Sep23-04, 07:11 PM
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Thanks for the advice tom. I actually have been reading this book called Trigonometry Demystified, from the Demystified series(similiar to For Dummies, and Complete Idiots Guide). It is a self teaching guide. I am two chapters into it and it is pretty easy. But I don't think that I am learning everything that I should. I want to buy a college text book and read it straight through. Do you think that would be better than this Demystefied book?
Next semester I am taking a College Algebra and Trig combination class, but I am afraid that I will not learn everything that I need to know, about the trig. I have a feeling that the class will be mostly college algebra with a little trig. I already know most of college algebra now, but I have to take that class to get the credit. I just really want to be ready for calculus. I take calculus 1 this summer.

Integral
#4
Sep23-04, 07:28 PM
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Self taught trig

You keep saying "read it straight through" as if it were a novel. Math Texts are not novels and should not be "read straight Through" you may well need to read and reread sections along with completing the exercises in each section.
Krazie
#5
Sep23-04, 07:36 PM
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Of course I would need to reread and study most of it. What I mean by read it straight through is not skip any chapters or any sections.
Krazie
#6
Sep23-04, 07:37 PM
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And yes do the problems too, I was thinking that in most sections I would do every other odd problem.
Tom McCurdy
#7
Sep23-04, 07:53 PM
P: 1,113
Trig although being a very useful tool, isn't the only thing you should have a good background for calculus... I generally don't consider Algerbra and Trig to be college level classes... I mean I took an Algerbra 2/Trig class at a college but it really wasn't college level. Is your calculus 1 class simliar to a precalculus?
because if you are worried about being prepared for calc

skim through a precalc book and see if you understand the material after you study some trig
Krazie
#8
Sep23-04, 08:16 PM
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i was not planning on taking a pre-calculus class. My college doen't actually offer one. And no, I never took it in high school. So you say that I should be more concerned about studying pre-calculus than trig as a pre-req. for calc 1?
Tom McCurdy
#9
Sep23-04, 08:26 PM
P: 1,113
Well no... you should have a Strong foundation in Trig... but precalc includes trig but ususally it assumes that you already know trig

Start learning trig then see if you can do the stuff in a precalc book
Krazie
#10
Sep23-04, 08:34 PM
P: n/a
That is exactly what I will do. Thanks for the advice Tom, it is greatly apreciated.
Tom McCurdy
#11
Sep23-04, 08:41 PM
P: 1,113
Your more than welcome, and again if you ever have any question private message me or just post it and I will try to help you
mathwonk
#12
Sep23-04, 09:31 PM
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i have taught calculus in college for over 35 years and no one has ever failed for not knowing trig. the main problem is algebra, and then geometry. the most important thing by far is to be good at algebra.

one other thing that also holds many people back is not knowing what a function is. i.e. most people think a function is a formula, rather than a pair, namely a domain, plus a rule for assigning values to each element of the domain.

so f(x) = 1/x defines a function on the domain of positive reals. and the additional rule that f(0) = 4, extends that to a function g defined on the non negative reals. I.e. then g(x) = 1/x if x is positive, and g(0) = 4. some people can never get it through their heads that it is ok to define a function anyway you want like this, using possibly several different rules for different parts of the domain.


but the main thing to know, above all things, is algebra.

trig takes about 5 minutes to learn. you only need to know the definitions of the two basic functions sin and cos, their relation to points and arcs on the circle, and then it helps to know the basic formulas, sin^2 + cos^2 = 1, and sin(x+y) = sin(x)cos(y) + sin(y)cos(x), and cos(x+y) = cos(x)cos(y) - sin(x)sin(y).

most people who have had trig do not even know these last two, (much less esoteric matter like the "law of cosines"),
just the basic one: sin^2 + cos^2 = 1.

but stuff like: why is [1/x - 1/a]/(x-a) = [a-x]/[(x-a)ax]? that is what stumps people.

or why is [a^(1/3) - b^(1/3)]/(a-b) =
[a-b]/[(a-b)(a^(2/3) + (ab)^(1/3) +b^(2/3)]?

its always the algebra. and this is needed every day in calculus. for example what good does it do to take a derivative and set it equal to zero, if you cannot solve it afterwards?


after the algebra it would help to know a couple basic things from geometry like similar triangles have proportional sides, and the pythagorean theorem. that's about it for geometry. of course it is nice to know a couple basic area and volume formulas, like the area of a circle, rectangle, cylinder, sphere, and triangle, but we usually review that stuff. the algebra never goes away. including the algebra of exponents.

like what is a^(1/3)? and what is (a^3 - b^3)/(a-b) ?

or (a^b)^c = ? or log(x^(10)) ?

from trig, i always have many people every year who fail to notice that since tan(x) = sin(x)/cos(x) that it is unbounded near where cos = 0. you do not need much trig to know that, just basics like do not divide by zero unless you expect something odd to happen. these people have had trig, they are just not thinking.
JasonRox
#13
Sep23-04, 09:47 PM
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Totally true, from what mathmonk said.

It is very important that you understand the fundamentals.

I taught myself Calculus, and now I am in 1st Year Calculus at a University. I learned a lot of knew stuff. I actually realized that I'm above average in the class, and some people are just lost. I also admit some parts I didn't know, and a function was one of them. I understand now. I knew that the derivative can be found using limits, while others completely forgot about First Principles.

I'm learning a lot, and it is unfortunate I skipped all my classes in high school.

Note: I also taught myself trigonometry, and physics. This is what I had to do because going back to high school wasn't an option. Now I'm a 1st year Physics/Math major. It's fun to see people brag about their math marks in high school, and I walk in and say "I HAD A SOLID 42%!".

The important thing is that, the one who takes the time to understand math (not just answer questions similiar to those in the book) will be the one who lasts.

PS. I hope I am that person. :)

Although you most likely will forget some trig identities, make sure you remember that you can derive them all using other identities you remember. Also, don't be discourage if you are a second year student and you forget something so simple like 0/0. Sometimes you are just thinking far too hard, 0/0 might seem like 1. A prof of mine said it is completely normal to just make a mistake like that.
Alkatran
#14
Sep24-04, 08:51 AM
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Quote Quote by mathwonk
one other thing that also holds many people back is not knowing what a function is. i.e. most people think a function is a formula, rather than a pair, namely a domain, plus a rule for assigning values to each element of the domain.
I taught myself computer programming (go QBasic help! ) and was actually surprised how SIMPLE math functions were. I was used to having a function... DO stuff... and not just return a value. So it was really like a step down.

So if you're taking calculus, I suggest learning to program first.

Oh... it helps with algebra, too.
matt grime
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Sep24-04, 09:06 AM
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Unless you're going to do something functional, programming will teach you bad habits, and even then it isn't a good idea. First, Alkatran, what is the definition of a function? Not something that just returns a 'value' for a start. Second, and my big bug bear, is that writing things like i=i+1 is unmathematical.
I'm an algebraist and I find writing programs most challenging: they do not tally.
DrWarezz
#16
Sep24-04, 09:21 AM
P: 33
programming will teach you bad habits, and even then it isn't a good idea.
I disagree. I'm quite young, and haven't had loads of maths experience.
I've taught myself DOS, HTML, JS, Java, C/C++ and am still learning more languages.
I found that programming has helped me ALOT. If I compare my mathematic ability now to before I learnt to program, I've improved dramatically. I also found that programming (especially the little bit of asm I've done) inspires me to do maths. :)

It also teached you about the use of different operands and functions and quite importantly; precedence.

Oh, and I also taught myseld trig (aswell as the sine and cosine rules). So, it definitely can be done :D

[r.D]
mathwonk
#17
Sep24-04, 09:43 PM
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the point is there is no such subject as trigonometry. there are basically two trig functions, sin and cos, and you should know something about these two functions.

Saying trigonometry is a subject is like saying x^2 is a subject, or maybe that quadratic functions are a subject.
HallsofIvy
#18
Sep25-04, 07:53 AM
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Quote Quote by mathwonk
the point is there is no such subject as trigonometry. there are basically two trig functions, sin and cos, and you should know something about these two functions.

Saying trigonometry is a subject is like saying x^2 is a subject, or maybe that quadratic functions are a subject.
That strikes me as a peculiar thing to say. It is not unusual for secondary schools or even colleges to have courses name "trigonometry" and certainly there are many textbooks on "trigonometry". Perhaps you are using the word "subject" in a very precise sense?

I would say that the subject, trigonometry, includes the 6 trig functions, sine, cosine, secant, cosecant, tangent, and cotangent (of course, all can be defined in terms of sine and cosine), methods of "solving" right triangles, methods of "solving" general triangles, and possibly some spherical geometry.


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