OK here's the deal: I want to start leasrning calculas because Algebra is getting too boring, and sence I'm only 15 the person who will be teaching me said I have to solve a problem befor he will teach me. So can someone teach me how to solve this? I said teach so it means more than just giving the answer, you have to tell me how it works. Here's what I have to answer: On top of the paper he drew a right triangle with all three sides different lengths. Under that he has this: Sin= Opposite/Hypotenuse Cos= Adjacent/Hypotenuse Tan= Opposite/Adjacent His question is: How does a calculator compute these functions? I remember reading about the ratio between the length of a triangles sides and the degrees of the algles, but I just can't remember all of it so I need help re-learning this.
Uses series, I think. sin x = x - x<sup>3</sup>/3! + x<sup>5</sup>/5! - x<sup>7</sup>/7! + ... cos x = 1 - x<sup>2</sup>/2! + x<sup>4</sup>/4! - x<sup>6</sup>/6! + ... etc. where x in radian.
Hi Mews, I guess your teacher is getting at something, but I'm damned if I know what it is. Have you used sin and cos in the equation of a unit circle yet?
Yes, I imagine you're right. But I'm not sure that this answers the question. Why do those series converge on the trig functions? You have to actually use calculus to determine the height of the opposite side as a function of the partial circumference of the arc of the circle defined by the angle. It seems to me that it begs the question. If you can figure out this problem, you don't need first-year calculus, you could be teaching it. I much preferred the Old Math. "For every epsilon there is a delta..." It was a bit dry but it made perfect sense.
To be honest, I would kind of listen to him. I am currently taking calculas and I'm 16, and believe me, it is not something that you would just want to jump into. It takes a firm knowledge of algebra, not to mention several important trig concepts. My best advice, study hard to algebra. Take geometry. Take algebra two. Take trigonometry. Take College Algebra (algebra 3, if available). Then go to calculus. You will be so much better off.
A rather unfair question for a 15 year old that does not know calculus yet, if you ask me. If you decide to learn calculus you will at some point learn how to approximate either of those functions using Taylor's formula.
I think the more common method is the CORDIC algorithm (I think this is actually the only method used in todays calculators). Some nice info on how it works: http://www.dspguru.com/info/faqs/cordic.htm This will be much more efficient than attempting to approximate with a series with the limited resources of a hand calculator. How anyone would expect a 15 year old, who is likely only vaguely aware of complex numbers, to come up with this would be a total mystery to me.
The reason I'm trying to learn Calculas is that Algebra has become too easy for me. Well I don't have much computer time so I'll look at the math stuff up at the top post when I have more time. I had alot of e-mails to go through and that took up most of my time so I'll have more time next time I get on, thanks for your help, I think. It may be a little too hard for me as I havn't seen complex problems like that excepts for when reading physics articles, wich I don't understand sometimes. Also I trying to find out if there's a conection between E=mc2 and the theory that nothing can travle faster than light and that's taking up most of my thoughts when I'm not thinking about my girlfriend.
Oh, well I never was good at spelling and I seem to do alot of misstypes. Well I'm going to look up a site that might be able to teach me calculus, I don't like computers teaching me because they might teach in a way my mind might not compute.
If you have some spare time and love math I can warmly recommend "Calculus - A Complete Course" by Robert A. Adams. It's a meaty book, but really cheap considering the amount of work put into it.
I'll see if the library has that book, but right now I'm reading Relativity: The Specail and General Theory, by Albery Einstien and than I'm going to read a science fiction book called Silkwood, it's a good book, good enuf to read twice in the same life-time. Also I'm working on a way to proove that matter can travle faster than the speed of light without the use of a black hole. I have too little work done to publish as of now, but I'm working real hard on it. If my work prooves successful than it'll be a new age in Astronomy and Physics.
lol, I am almost done with calc 3 and I still have no idea how to explain that! =] I think I should have paid more attention in calc 2, thats probably where I would have "lernt" it.
General Relativity - Yeah, I gave up, after i got to tensor calculus. maybe I should pick it up again now that I'm taking calc in school?
MewSkitty: I started learning calculus when I was 15, so I say go for it! The McLaurin series' that Paul T mentioned are correct, and are obtained by forming an infinite series for sin x is in increasing powers of x, where the the n-th power of x has the coefficient of the n-th derivative of sin x wrt x at 0 divided by n! The derivative is a measure of the rate of change of the graph, so the first derivative is the gradient of the graph in terms of x, the second derivative is the rate of change of the gradient, and so on. The derivative is the basis of calculus, but they're pretty easy, it's the integral you've got to watch out for! Fraggle: I know what you mean about epsilon delta notation, it's nice to see it and think "so that's why that works".
