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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: HungTran2009 on March 13, 2010, 02:44:05 pm

Title: Parametric Equations :D
Post by: HungTran2009 on March 13, 2010, 02:44:05 pm: I need to find the Cartesian equation of the curve with the following parametric equation:

x=cos(2t)-2 and y=3+2sin(2t), t∈[0, pi/2]

The book I'm using (MQ 3rd edition) tells me that the graph is the "top half" of an ellipse. Why is this? I know it has something to do with the "t∈[0, pi/2]" part...but I thought that the angle would've been pi instead...

Thanks
Title: Re: Parametric Equations :D
Post by: m@tty on March 13, 2010, 02:58:46 pm: $t\in[0,\frac{\pi}{2}]$
$2t\in[0,\pi]$

$\therefore x\in[-3,-1]$
and
$y\in[3,5]$

Which is only the top half of the ellipse

$(x+2)^2+\frac{(y-3)^2}{4}=1$
Title: Re: Parametric Equations :D
Post by: HungTran2009 on March 13, 2010, 03:40:51 pm: OHHHHHHH :D

Thanks for the help!
And thanks for replying!