How to use inner product to find angle? Linear Algebra [on hold]
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Let C[0, π] denote the set of real-valued continuous functions on [0, π].
Define an inner product on C[0, π] by
(f, g)C[0,π] ≡ $$int_0^π f(x)g(x)dx$$.
Use this inner product to determine the angle between sin x and x.
linear-algebra
asked yesterday
Zhe Tian
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put on hold as off-topic by José Carlos Santos, Masacroso, 5xum, amWhy, Delta-u yesterday
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Let C[0, π] denote the set of real-valued continuous functions on [0, π].
Define an inner product on C[0, π] by
(f, g)C[0,π] ≡ $$int_0^π f(x)g(x)dx$$.
Use this inner product to determine the angle between sin x and x.
linear-algebra
asked yesterday
Zhe Tian
6
New contributor
Zhe Tian is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by José Carlos Santos, Masacroso, 5xum, amWhy, Delta-u yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, Masacroso, 5xum, amWhy, Delta-u
If this question can be reworded to fit the rules in the help center, please edit the question.
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up vote
0
down vote
favorite
up vote
0
down vote
favorite
Let C[0, π] denote the set of real-valued continuous functions on [0, π].
Define an inner product on C[0, π] by
(f, g)C[0,π] ≡ $$int_0^π f(x)g(x)dx$$.
Use this inner product to determine the angle between sin x and x.
linear-algebra
asked yesterday
Zhe Tian
6
New contributor
Zhe Tian is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Let C[0, π] denote the set of real-valued continuous functions on [0, π].
Define an inner product on C[0, π] by
(f, g)C[0,π] ≡ $$int_0^π f(x)g(x)dx$$.
Use this inner product to determine the angle between sin x and x.
linear-algebra
linear-algebra
asked yesterday
Zhe Tian
6
New contributor
Zhe Tian is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
Zhe Tian
6
New contributor
Zhe Tian is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
Zhe Tian
6
New contributor
Zhe Tian is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
Zhe Tian
6
asked yesterday
Zhe Tian
6
6
New contributor
Zhe Tian is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Zhe Tian is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Zhe Tian is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by José Carlos Santos, Masacroso, 5xum, amWhy, Delta-u yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, Masacroso, 5xum, amWhy, Delta-u
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by José Carlos Santos, Masacroso, 5xum, amWhy, Delta-u yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, Masacroso, 5xum, amWhy, Delta-u
If this question can be reworded to fit the rules in the help center, please edit the question.
3
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
yesterday
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3
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
yesterday
3
3
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
yesterday
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
yesterday
add a comment |
2 Answers
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You know that $$langle f,grangle = int_0^pi f(x)g(x),dx,$$ and the formula for the angle between two elements $u, v$ in an inner product space $V$ is given by $$costheta = {langle u, vrangleover|u||v|}.$$ Observe that if $u = sin(x)$ and $v = x$, then $$|u|^2 = {langle u,urangle} = {int_0^pisin^2(x),dx} = {pi/2},$$ $$|v|^2 = langle v, vrangle = int_0^pi x^2,dx = {pi^3over3}.$$ I leave it to you to compute the remainder of the parts and apply inverse cosine to determine the angle.
answered yesterday
Decaf-Math
3,027825
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1
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HINT
Recall that
$$costheta=frac{langle u,vrangle}{sqrt{langle u,urangle}cdotsqrt{langle v,vrangle}}$$
answered yesterday
gimusi
84.2k74292
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
You know that $$langle f,grangle = int_0^pi f(x)g(x),dx,$$ and the formula for the angle between two elements $u, v$ in an inner product space $V$ is given by $$costheta = {langle u, vrangleover|u||v|}.$$ Observe that if $u = sin(x)$ and $v = x$, then $$|u|^2 = {langle u,urangle} = {int_0^pisin^2(x),dx} = {pi/2},$$ $$|v|^2 = langle v, vrangle = int_0^pi x^2,dx = {pi^3over3}.$$ I leave it to you to compute the remainder of the parts and apply inverse cosine to determine the angle.
answered yesterday
Decaf-Math
3,027825
add a comment |
up vote
2
down vote
You know that $$langle f,grangle = int_0^pi f(x)g(x),dx,$$ and the formula for the angle between two elements $u, v$ in an inner product space $V$ is given by $$costheta = {langle u, vrangleover|u||v|}.$$ Observe that if $u = sin(x)$ and $v = x$, then $$|u|^2 = {langle u,urangle} = {int_0^pisin^2(x),dx} = {pi/2},$$ $$|v|^2 = langle v, vrangle = int_0^pi x^2,dx = {pi^3over3}.$$ I leave it to you to compute the remainder of the parts and apply inverse cosine to determine the angle.
answered yesterday
Decaf-Math
3,027825
add a comment |
up vote
2
down vote
up vote
2
down vote
You know that $$langle f,grangle = int_0^pi f(x)g(x),dx,$$ and the formula for the angle between two elements $u, v$ in an inner product space $V$ is given by $$costheta = {langle u, vrangleover|u||v|}.$$ Observe that if $u = sin(x)$ and $v = x$, then $$|u|^2 = {langle u,urangle} = {int_0^pisin^2(x),dx} = {pi/2},$$ $$|v|^2 = langle v, vrangle = int_0^pi x^2,dx = {pi^3over3}.$$ I leave it to you to compute the remainder of the parts and apply inverse cosine to determine the angle.
answered yesterday
Decaf-Math
3,027825
You know that $$langle f,grangle = int_0^pi f(x)g(x),dx,$$ and the formula for the angle between two elements $u, v$ in an inner product space $V$ is given by $$costheta = {langle u, vrangleover|u||v|}.$$ Observe that if $u = sin(x)$ and $v = x$, then $$|u|^2 = {langle u,urangle} = {int_0^pisin^2(x),dx} = {pi/2},$$ $$|v|^2 = langle v, vrangle = int_0^pi x^2,dx = {pi^3over3}.$$ I leave it to you to compute the remainder of the parts and apply inverse cosine to determine the angle.
answered yesterday
Decaf-Math
3,027825
edited 17 hours ago
answered yesterday
Decaf-Math
3,027825
answered yesterday
Decaf-Math
3,027825
answered yesterday
Decaf-Math
3,027825
3,027825
add a comment |
add a comment |
up vote
1
down vote
HINT
Recall that
$$costheta=frac{langle u,vrangle}{sqrt{langle u,urangle}cdotsqrt{langle v,vrangle}}$$
answered yesterday
gimusi
84.2k74292
add a comment |
up vote
1
down vote
HINT
Recall that
$$costheta=frac{langle u,vrangle}{sqrt{langle u,urangle}cdotsqrt{langle v,vrangle}}$$
answered yesterday
gimusi
84.2k74292
add a comment |
up vote
1
down vote
up vote
1
down vote
HINT
Recall that
$$costheta=frac{langle u,vrangle}{sqrt{langle u,urangle}cdotsqrt{langle v,vrangle}}$$
answered yesterday
gimusi
84.2k74292
HINT
Recall that
$$costheta=frac{langle u,vrangle}{sqrt{langle u,urangle}cdotsqrt{langle v,vrangle}}$$
answered yesterday
gimusi
84.2k74292
answered yesterday
gimusi
84.2k74292
answered yesterday
gimusi
84.2k74292
answered yesterday
gimusi
84.2k74292
84.2k74292
add a comment |
add a comment |
3
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
yesterday