Sarahisme Posted August 1, 2005 Share Posted August 1, 2005 hi all , i can't figure out how i am ment to use the stated fact about tan x. the way i'd do it is dividing the series expansion for cos(x) into that for sin(x)... but yeah i dunno any advice would be greatly appreciated __sarah__ Link to comment Share on other sites More sharing options...
Sarahisme Posted August 1, 2005 Author Share Posted August 1, 2005 there is second part to this question, and again i could do it by other means, but not using the given fact this is the second part to the question: Link to comment Share on other sites More sharing options...
DQW Posted August 1, 2005 Share Posted August 1, 2005 (a) You are given two things. The FIRST thing that would come to my mind is to substitute the first into the second ... (b) Having said (a), I shouldn't say anything more. Sarah, these are nothing more than direct substitution problems. Link to comment Share on other sites More sharing options...
Sarahisme Posted August 1, 2005 Author Share Posted August 1, 2005 but part a says to use the first fact, not the second (or both) ... or are you talking about doing part b? Link to comment Share on other sites More sharing options...
Sarahisme Posted August 1, 2005 Author Share Posted August 1, 2005 sorry to be such a panicky hassle sort of thing, this si just about the most stresfull week so far this year! Link to comment Share on other sites More sharing options...
DQW Posted August 1, 2005 Share Posted August 1, 2005 (a) You are given 2 things : 1. tan(x) is analytic in (-pi/2, pi/2) 2. tan(x) is odd Substitute the expansion (from 1) in the equation for 2. Link to comment Share on other sites More sharing options...
Sarahisme Posted August 1, 2005 Author Share Posted August 1, 2005 ok i have so i get tan'(x)= 1 + tan^{2}(-x) but i dont see how this helps... (although i am sure it does ) Link to comment Share on other sites More sharing options...
Sarahisme Posted August 1, 2005 Author Share Posted August 1, 2005 oh wait its like an identity or something, 1 + tan^{2} = sec^{2) or something like that, damn i wish i had textbook with me right now Link to comment Share on other sites More sharing options...
DQW Posted August 1, 2005 Share Posted August 1, 2005 I was talking about part (a), not part (b) Apply the power series expansion to each side of the given equation (the "fact"). What do you get ? Link to comment Share on other sites More sharing options...
Sarahisme Posted August 1, 2005 Author Share Posted August 1, 2005 this? i gotta run though i'll be back in a few hours...sorry Picture 1.pdf Link to comment Share on other sites More sharing options...
Sarahisme Posted August 1, 2005 Author Share Posted August 1, 2005 or is it this...because this makes more sense to me.... Picture 2.pdf Link to comment Share on other sites More sharing options...
Sarahisme Posted August 2, 2005 Author Share Posted August 2, 2005 oh ok then you expand it like this.... therefore all n even terms are zero (assuming you start from n = 1 right?) lol....now for part b! dammit Link to comment Share on other sites More sharing options...
DQW Posted August 2, 2005 Share Posted August 2, 2005 How do you show that the even terms are zero ? It does not matter what value of n you start from, for the even terms to vanish (but in any case, you start with n=0 because that term is part of a general power series). Link to comment Share on other sites More sharing options...
Sarahisme Posted August 2, 2005 Author Share Posted August 2, 2005 when i said "oh ok then you expand it like this...." i ment to post this along with it... Link to comment Share on other sites More sharing options...
Sarahisme Posted August 2, 2005 Author Share Posted August 2, 2005 i tried a similar method for part (b) but i don't know how to expand the square of a infinite sum... Link to comment Share on other sites More sharing options...
Sarahisme Posted August 2, 2005 Author Share Posted August 2, 2005 ok so i have got this much so far for part (b), but as i said before i then get a infinte sum squared and i don't know how to deal with such a thing! Link to comment Share on other sites More sharing options...
DQW Posted August 2, 2005 Share Posted August 2, 2005 (a) You have a tiny error in post #14. Why did a_0 change signs on the RHS ? (b) You are not asked for all the coefficients, right ? So, just write out the first few terms (I'll let you figure out how many you need to write), square it, and compare coefficients. Link to comment Share on other sites More sharing options...
Sarahisme Posted August 3, 2005 Author Share Posted August 3, 2005 you mean end up with things such as (a_1)^{2} = 3(a_3) ?? Link to comment Share on other sites More sharing options...
DQW Posted August 3, 2005 Share Posted August 3, 2005 I couldn't comment on that unless I know how you got it. Link to comment Share on other sites More sharing options...
Sarahisme Posted August 3, 2005 Author Share Posted August 3, 2005 oh sorry, yep hang on... Link to comment Share on other sites More sharing options...
Sarahisme Posted August 3, 2005 Author Share Posted August 3, 2005 (a) You have a tiny error in post #14. Why did a_0 change signs on the RHS ? oh ok so a_0 is zero aswell (like all the even n terms)? Link to comment Share on other sites More sharing options...
Sarahisme Posted August 3, 2005 Author Share Posted August 3, 2005 ok so post #14 should have been this.... Link to comment Share on other sites More sharing options...
Sarahisme Posted August 3, 2005 Author Share Posted August 3, 2005 ok so this is what i do to expand it, but then well yep i don't know how you would compare terms with this... :S Link to comment Share on other sites More sharing options...
Sarahisme Posted August 3, 2005 Author Share Posted August 3, 2005 wait second....may have eureka moment here....!!! Link to comment Share on other sites More sharing options...
Sarahisme Posted August 3, 2005 Author Share Posted August 3, 2005 ok got it i think, i was on the right track........here we go ! Link to comment Share on other sites More sharing options...
Recommended Posts
Create an account or sign in to comment
You need to be a member in order to leave a comment
Create an account
Sign up for a new account in our community. It's easy!
Register a new accountSign in
Already have an account? Sign in here.
Sign In Now