Represent the plane curve by a vector-valued function. ${x}^{2}+{y}^{2}=25$

inlays85k5
2021-11-23
Answered

Represent the plane curve by a vector-valued function. ${x}^{2}+{y}^{2}=25$

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memomzungup4

Answered 2021-11-24
Author has **14** answers

Step 1

It is given that,${x}^{2}+{y}^{2}=25$

Let$x=5\mathrm{cos}t$ and $y=\mathrm{sin}t$ , Then

${\left(5\mathrm{cos}t\right)}^{2}+{\left(5\mathrm{sin}t\right)}^{2}=25({\mathrm{cos}}^{2}\left(t\right)+{\mathrm{sin}}^{2}\left(t\right))$

$=25$

Step 2

The function of the form$r\left(t\right)=x\left(t\right)i+y\left(t\right)j$ is a vector valued function.

Substitute x and y in the above equation, to get

$r\left(t\right)=\left(5\mathrm{cos}t\right)i+\left(5\mathrm{sin}t\right)j$

It is given that,

Let

Step 2

The function of the form

Substitute x and y in the above equation, to get

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