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

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To parametrize the function y = sin(x) in component form, one can set x = t, leading to the parameterization r(t) = ti + sin(t)j. This approach is valid as it expresses y as a function of t, maintaining the relationship between x and y. The general form for such parameterizations is x = t and y = f(t), represented as t*i + f(t)*j. The discussion confirms that this method is a straightforward way to achieve the desired component form. Understanding this parameterization is essential for working with functions in vector notation.
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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