Math Is Fun Forum

Danbee

Member

Registered: 2008-08-28

Posts: 21

Polar coordinates and parametric equations

Find the rectangular equation for this curve:

y=cos2t, y=sin2t; π≤t≤π

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Polar coordinates and parametric equations

i'm guessing you mean x = cos2t ^^

you can immediately see that that is the equation of a circle, but if you need to show it algebraicaly

x = cos2t
t = ½cos-¹x

y = sin(cos-¹x)
x² + y² = 1
or
y = ±√(1-x²)
if you want y as a function of x

if you don't know how to do the last step:

y = sin(A), A = cos-¹x
y = sin(A), x = cos(A)
x² + y² = 1  (sin²A + cos²A = 1)
y = ±√(1-x²)

Last edited by luca-deltodesco (2008-09-13 17:45:06)

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