Register to reply

Cosine function

by sara_87
Tags: cosine, function
Share this thread:
sara_87
#1
Dec22-08, 05:58 AM
P: 774
1. The problem statement, all variables and given/known data

what is cos(2n*pi)

2. Relevant equations



3. The attempt at a solution

I understand that cos(npi)=(-1)^n
so is cos(2n*pi)=2(-1)^n ??
Phys.Org News Partner Science news on Phys.org
Wildfires and other burns play bigger role in climate change, professor finds
SR Labs research to expose BadUSB next week in Vegas
New study advances 'DNA revolution,' tells butterflies' evolutionary history
cristo
#2
Dec22-08, 06:19 AM
Mentor
cristo's Avatar
P: 8,306
Make the substitution m=2n in cos(mπ)=(-1)^m
sara_87
#3
Dec22-08, 06:53 AM
P: 774
so you mean cos(2n^2)=(-1)^2n
??

cristo
#4
Dec22-08, 06:54 AM
Mentor
cristo's Avatar
P: 8,306
Cosine function

No, I mean cos(2n pi)=(-1)^{2n}
HallsofIvy
#5
Dec22-08, 07:19 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,361
Do you know what cos(0) is? Do you know that cosine is periodic with period 2 pi?
sara_87
#6
Dec22-08, 07:23 AM
P: 774
yep cos0=1
yep, cos is periodic with period 2pi
HallsofIvy
#7
Dec22-08, 08:29 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,361
So cos(2n pi)= cos(0+ n(2pi))= ?
sara_87
#8
Dec23-08, 09:33 AM
P: 774
oh right,
so =(-1)^(n+1)
is that right?
Mark44
#9
Dec23-08, 10:22 AM
Mentor
P: 21,214
Quote Quote by sara_87 View Post
oh right,
so =(-1)^(n+1)
is that right?
No. Look at posts 4 and 7.
HallsofIvy
#10
Dec23-08, 10:58 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,361
Quote Quote by HallsofIvy View Post
Do you know what cos(0) is? Do you know that cosine is periodic with period 2 pi?
Quote Quote by sara_87 View Post
yep cos0=1
yep, cos is periodic with period 2pi
Quote Quote by HallsofIvy View Post
So cos(2n pi)= cos(0+ n(2pi))= ?
Quote Quote by sara_87 View Post
oh right,
so =(-1)^(n+1)
is that right?
Okay, what does "periodic" mean????
boombaby
#11
Dec23-08, 11:05 PM
P: 130
...I think it is necessary to know the graph of cos(x), which may help a lot. so, find one.

edit ( trying not to be ambiguous)
...I think it is necessary for one to know the graph of cos(x), which may also help a lot. (regardless of this particular problem)...
"periodic" is really the key
HallsofIvy
#12
Dec24-08, 05:25 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,361
It might help. It is not necessary. All that is necessary is to know what "periodic" means. No computation is required.
sara_87
#13
Dec24-08, 02:48 PM
P: 774
I understand that periodic means that cosine function repeats after multiples of 2 pi. but how would that have anything to do with writing cos(2n*pi) ?
cos (npi)=(-1)^n because as long as n is an integer, the value will alternate from -1 and 1 (clearly form the graph)
HallsofIvy
#14
Dec24-08, 04:18 PM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,361
Quote Quote by sara_87 View Post
I understand that periodic means that cosine function repeats after multiples of 2 pi. but how would that have anything to do with writing cos(2n*pi) ?
Would it be easier if it were written n*(2pi) rather than 2n*pi? This is about multiples of 2pi!

cos(2pi)= cos(0+ 2pi)= cos(0)= 1

cos(4pi)= cos(2pi+ 2pi)= cos(2pi)= 1

cos(6pi)= cos(4pi+ 2pi)= cos(4pi)= 1

cos (npi)=(-1)^n because as long as n is an integer, the value will alternate from -1 and 1 (clearly form the graph)
sara_87
#15
Dec24-08, 05:11 PM
P: 774
oh right!!! so cos(n2pi) has to always be 1...i feel very stupid, i should have known that. for all n, cos(2npi) must be 1 as long as n is an integer.

thank you very much


Register to reply

Related Discussions
Cosine function & Modelling Tides Calculus & Beyond Homework 4
Finding the maximum and minimum points of a cosine function... Calculus & Beyond Homework 9
Normalization of a wave function with cosine Advanced Physics Homework 6
How do you solve for the intersection of a line and a cosine function? Calculus 6
Linear Combination of Cosine Function Precalculus Mathematics Homework 1