Question

Eliminate the parameter

x = 3 cos t, y = 3 sin t

Hi an explanation on how to go about this would be much appreciated!

Answer 1

recall the famous identity \(\cos^2(t)+\sin^2(t)=1\)

Answer 2

2 of my favorite OpenStudyers typing, this makes me happy! Thanks for the wanting to help @satellite73 and @vishweshshrimali5

And yes I know there's something I need to do with that identity but I'm unsure

Answer 3

do it!

Answer 4

no dear, just square and add
do it
write
\[x^2+y^2=...\] and you will see the \(t\) magically disappear

Answer 5

i made a typo there
square \(3\cos(t)\) and square \(3\sin(t)\) and add them up

Answer 6

let me know what you get
then we will see why you knew the answer to begin with

Answer 7

Uhm I'm not sure because I'm not fully understanding.

But if I squared both wouldn't I get

9cos^2+9sin^2t

Answer 8

yes !

Answer 9

Question:

Why are we even adding them?

Answer 10

that means
\[x^2+y^2=9\cos^2(x)+9\sin^2(x)\]
factor the \(9\) from the right hand side

Answer 11

i will answer after you do it and see the \(t\) go bye bye

Answer 12

x^2+y^2=9(1)

Answer 13

yay
the t is gone and you see that you have a circle of radius 3

Answer 14

Is that eliminating the parameter? So that's all I had to do?

Answer 15

you knew this before you started the problem
the unit circle has points \((x,y)\) that sastifies the equation \(x^2+y^2=1\)
they are also given by the points \((\cos(t), \sin(t))\) i.e. parametrized by the "angle"

Answer 16

yes, that is all you have to do
you had the parameter \(t\) in \(x=3\cos(t), y = 3\sin(t)\)
now you have
\[x^2+y^2=9\] the parameter is gone

Answer 17

if it as \[x=\cos(t),y=\sin(t)\] it is the unit circle
multiplying by 3 makes the radius 3 instead of 1

Answer 18

Oh okay, thank you :)

Answer 19

I was going to reply the same thing but @satellite73 stole my answer :P

Thanks for thinking of so highly of me @marissalovescats

Answer 20

yw
with a little practice you will do this in your head
i realize you might think at the beginning that there is some one method for "eliminating the parameter" but there is not really one way to do it

Answer 21

I think highly of all!

Answer 22

That's a good thing but never underestimate your self.

So, got the answer ?

Answer 23

Yup, I did!

Answer 24

This is the graphical solution :)