Parametrize y = sin(x) with i^ j^ components

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Discussion Overview

The discussion focuses on how to parametrize the function y = sin(x) into component form using vector notation, specifically in terms of i and j components. The scope includes mathematical reasoning and technical explanation.

Discussion Character

  • Mathematical reasoning, Technical explanation

Main Points Raised

  • One participant expresses difficulty in understanding the parametrization of y = sin(x) into component form.
  • Another participant suggests letting x = t as a hint for parametrization.
  • A participant proposes the parametrization r(t) = ti^ + sin(t)j^ and seeks confirmation on its validity.
  • A later reply indicates that the proposed parametrization looks good to them.
  • Another participant states that as long as y is a function of t, the "trivial" parameterization can be expressed as x = t, y = f(t), or in vector terms t\vec{i} + f(t)\vec{j}.

Areas of Agreement / Disagreement

Participants generally agree on the approach to parametrization, with some confirming the proposed forms, but no consensus on a singular method is established.

Contextual Notes

The discussion does not clarify any assumptions regarding the definitions of the components or the context of the parametrization.

Who May Find This Useful

Readers interested in mathematical parametrization, vector calculus, or those seeking clarification on representing functions in component form may find this discussion useful.

kgal
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I am having a hard time understanding how to parametrize the function y = sin(x) into component form (i,j).
 
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kgal said:
I am having a hard time understanding how to parametrize the function y = sin(x) into component form (i,j).

Hey kgal and welcome to the forums.

Hint: let x = t.
 
Thanks,

is it r(t) = ti^ +sin(t)j^ ?
 
kgal said:
Thanks,

is it r(t) = ti^ +sin(t)j^ ?

That looks pretty good to me :)
 
As long as y is a function of t, y= f(t), there is the "trivial" parameterization, x= t, y= f(t) or, in vector terms t\vec{i}+ f(t)\vec{j}.
 

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