Does $cosleft(frac{2pi}2right) = 0$?
up vote
0
down vote
favorite
I am studying chapter 10 (Partial Differential Equations and Fourier Series) of Boyce's Elementary Differential Equations and I stumbled upon this question:
Consider the conduction of heat in a rod $40~rm cm$ in length whose ends are maintained at $0^circrm C$ for
all $t > 0$. In the below question find an expression for the temperature $u(x, t)$ if the initial temperature distribution in the rod is the given function. Suppose that $α_2 = 1$.
$u(x, 0) = begin{cases}
x & 0 le x lt20\
40-x & 20 le x le40\
end{cases}
\$
While I was checking the soluotion of this question I found online I saw in one of the steps involved below is treated as zero:
$$cosfrac{frac{(npi L)}{2}}{L} = 0.$$
I just wish to ask why is that the case that the above equals zero? For instance if $n = 2$ shouldn't the above equals $cos(pi) = -1$?
Thank you!
*this link is a screenshot of the solution I found online:
!https://imgur.com/pLHwZHe ; link to the full solution is here: !https://math.berkeley.edu/~ogus/old/Math_54-05/HW%20solutions/homework509.pdf
trigonometry pde fourier-series
edited Nov 26 at 15:19
Davide Giraudo
124k16150258
asked Nov 26 at 10:23
Lullaby
42
add a comment |
up vote
0
down vote
favorite
I am studying chapter 10 (Partial Differential Equations and Fourier Series) of Boyce's Elementary Differential Equations and I stumbled upon this question:
Consider the conduction of heat in a rod $40~rm cm$ in length whose ends are maintained at $0^circrm C$ for
all $t > 0$. In the below question find an expression for the temperature $u(x, t)$ if the initial temperature distribution in the rod is the given function. Suppose that $α_2 = 1$.
$u(x, 0) = begin{cases}
x & 0 le x lt20\
40-x & 20 le x le40\
end{cases}
\$
While I was checking the soluotion of this question I found online I saw in one of the steps involved below is treated as zero:
$$cosfrac{frac{(npi L)}{2}}{L} = 0.$$
I just wish to ask why is that the case that the above equals zero? For instance if $n = 2$ shouldn't the above equals $cos(pi) = -1$?
Thank you!
*this link is a screenshot of the solution I found online:
!https://imgur.com/pLHwZHe ; link to the full solution is here: !https://math.berkeley.edu/~ogus/old/Math_54-05/HW%20solutions/homework509.pdf
trigonometry pde fourier-series
edited Nov 26 at 15:19
Davide Giraudo
124k16150258
asked Nov 26 at 10:23
Lullaby
42
1
Your links say $cos frac{npi L/2}{L}$, not what you wrote.
– Ennar
Nov 26 at 10:38
Thanks for pointing it out I think it's changed by Tianlalu while he's correcting a bunch of formatting error I made... let me change it back thanks both of you
– Lullaby
Nov 26 at 10:43
Ah, I see, yes. I don't understand why they would deliberately change the meaning without confirming with you. As to the question, the expression is $0$ for odd $n$.
– Ennar
Nov 26 at 10:48
$n$ is an odd integer.
– Alex Silva
Nov 26 at 10:48
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I am studying chapter 10 (Partial Differential Equations and Fourier Series) of Boyce's Elementary Differential Equations and I stumbled upon this question:
Consider the conduction of heat in a rod $40~rm cm$ in length whose ends are maintained at $0^circrm C$ for
all $t > 0$. In the below question find an expression for the temperature $u(x, t)$ if the initial temperature distribution in the rod is the given function. Suppose that $α_2 = 1$.
$u(x, 0) = begin{cases}
x & 0 le x lt20\
40-x & 20 le x le40\
end{cases}
\$
While I was checking the soluotion of this question I found online I saw in one of the steps involved below is treated as zero:
$$cosfrac{frac{(npi L)}{2}}{L} = 0.$$
I just wish to ask why is that the case that the above equals zero? For instance if $n = 2$ shouldn't the above equals $cos(pi) = -1$?
Thank you!
*this link is a screenshot of the solution I found online:
!https://imgur.com/pLHwZHe ; link to the full solution is here: !https://math.berkeley.edu/~ogus/old/Math_54-05/HW%20solutions/homework509.pdf
trigonometry pde fourier-series
edited Nov 26 at 15:19
Davide Giraudo
124k16150258
asked Nov 26 at 10:23
Lullaby
42
I am studying chapter 10 (Partial Differential Equations and Fourier Series) of Boyce's Elementary Differential Equations and I stumbled upon this question:
Consider the conduction of heat in a rod $40~rm cm$ in length whose ends are maintained at $0^circrm C$ for
all $t > 0$. In the below question find an expression for the temperature $u(x, t)$ if the initial temperature distribution in the rod is the given function. Suppose that $α_2 = 1$.
$u(x, 0) = begin{cases}
x & 0 le x lt20\
40-x & 20 le x le40\
end{cases}
\$
While I was checking the soluotion of this question I found online I saw in one of the steps involved below is treated as zero:
$$cosfrac{frac{(npi L)}{2}}{L} = 0.$$
I just wish to ask why is that the case that the above equals zero? For instance if $n = 2$ shouldn't the above equals $cos(pi) = -1$?
Thank you!
*this link is a screenshot of the solution I found online:
!https://imgur.com/pLHwZHe ; link to the full solution is here: !https://math.berkeley.edu/~ogus/old/Math_54-05/HW%20solutions/homework509.pdf
trigonometry pde fourier-series
trigonometry pde fourier-series
edited Nov 26 at 15:19
Davide Giraudo
124k16150258
asked Nov 26 at 10:23
Lullaby
42
edited Nov 26 at 15:19
Davide Giraudo
124k16150258
asked Nov 26 at 10:23
Lullaby
42
edited Nov 26 at 15:19
Davide Giraudo
124k16150258
edited Nov 26 at 15:19
Davide Giraudo
124k16150258
edited Nov 26 at 15:19
Davide Giraudo
124k16150258
124k16150258
asked Nov 26 at 10:23
Lullaby
42
asked Nov 26 at 10:23
Lullaby
42
asked Nov 26 at 10:23
Lullaby
42
42
1
Your links say $cos frac{npi L/2}{L}$, not what you wrote.
– Ennar
Nov 26 at 10:38
Thanks for pointing it out I think it's changed by Tianlalu while he's correcting a bunch of formatting error I made... let me change it back thanks both of you
– Lullaby
Nov 26 at 10:43
Ah, I see, yes. I don't understand why they would deliberately change the meaning without confirming with you. As to the question, the expression is $0$ for odd $n$.
– Ennar
Nov 26 at 10:48
$n$ is an odd integer.
– Alex Silva
Nov 26 at 10:48
add a comment |
1
Your links say $cos frac{npi L/2}{L}$, not what you wrote.
– Ennar
Nov 26 at 10:38
Thanks for pointing it out I think it's changed by Tianlalu while he's correcting a bunch of formatting error I made... let me change it back thanks both of you
– Lullaby
Nov 26 at 10:43
Ah, I see, yes. I don't understand why they would deliberately change the meaning without confirming with you. As to the question, the expression is $0$ for odd $n$.
– Ennar
Nov 26 at 10:48
$n$ is an odd integer.
– Alex Silva
Nov 26 at 10:48
1
1
Your links say $cos frac{npi L/2}{L}$, not what you wrote.
– Ennar
Nov 26 at 10:38
Your links say $cos frac{npi L/2}{L}$, not what you wrote.
– Ennar
Nov 26 at 10:38
Thanks for pointing it out I think it's changed by Tianlalu while he's correcting a bunch of formatting error I made... let me change it back thanks both of you
– Lullaby
Nov 26 at 10:43
Thanks for pointing it out I think it's changed by Tianlalu while he's correcting a bunch of formatting error I made... let me change it back thanks both of you
– Lullaby
Nov 26 at 10:43
Ah, I see, yes. I don't understand why they would deliberately change the meaning without confirming with you. As to the question, the expression is $0$ for odd $n$.
– Ennar
Nov 26 at 10:48
Ah, I see, yes. I don't understand why they would deliberately change the meaning without confirming with you. As to the question, the expression is $0$ for odd $n$.
– Ennar
Nov 26 at 10:48
$n$ is an odd integer.
– Alex Silva
Nov 26 at 10:48
$n$ is an odd integer.
– Alex Silva
Nov 26 at 10:48
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3014155%2fdoes-cos-left-frac2-pi2-right-0%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
1
Your links say $cos frac{npi L/2}{L}$, not what you wrote.
– Ennar
Nov 26 at 10:38
Thanks for pointing it out I think it's changed by Tianlalu while he's correcting a bunch of formatting error I made... let me change it back thanks both of you
– Lullaby
Nov 26 at 10:43
Ah, I see, yes. I don't understand why they would deliberately change the meaning without confirming with you. As to the question, the expression is $0$ for odd $n$.
– Ennar
Nov 26 at 10:48
$n$ is an odd integer.
– Alex Silva
Nov 26 at 10:48