Eliminate t to give an equation that relates x and y:

x=cos(t)http://nernst.chem.sfu.ca/adm/jsMath...120/char3B.pngy=sin2(t)−3

y= ??

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- Nov 18th 2008, 08:42 AMgearshifterRelating X and Y
Eliminate t to give an equation that relates x and y:

x=cos(t)http://nernst.chem.sfu.ca/adm/jsMath...120/char3B.pngy=sin2(t)−3

y= ?? - Nov 18th 2008, 10:01 AMAryth
Remember the identity:

$\displaystyle \sin^2{t} + \cos^2{t} = 1$

So:

$\displaystyle sin^2{t} = 1 - \cos^2{t}$

$\displaystyle y = 1 - \cos^2{t} - 3$

$\displaystyle y = -\cos^2{t} - 2$

Now we look at x:

$\displaystyle x = \cos{t}$

Square both sides:

$\displaystyle x^2 = \cos^2{t}$

Multiply both sides by -1:

$\displaystyle -x^2 = -\cos^2{t}$

Now, subtract both sides by 2:

$\displaystyle -x^2 - 2 = -\cos^2{t} - 2$

We know that:

$\displaystyle y = -\cos^2{t} - 2$

So, we get:

$\displaystyle y = -x^2 - 2$

And there you go. - Nov 18th 2008, 10:16 AMearboth
- Nov 18th 2008, 07:55 PMgearshifter
wow thanks. I was stuck on that for sometime because i didnt know how to relate it!