Parametric to Rectangular?
posted by Tabby .
find the rectangular eqaution of the curve whose parametric equations are x=5cos2T and y=sin2T, where 0 is less than/equal to T which is less than/equal to 180

from x = 5cos 2T > cos 2T = x/5
from y = sin 2T > sin 2T = y
we know sin^2 2T + cos^2 2T= 1
x^2 /25 + y^2 = 1
x^2 + 25y^2 = 25
(looks like we have an ellipse)
test:
let T = 30°
x = 5cos60° = 5(1/2) = 5/2
y = sin60° = √3/2
sub into the rectangular...
LS = 25/4 + 25(3/4) = 100/4 = 25
let T = 19.6°
x = 5cos39.2· = appr. 3.8747
y = sin39.2 = appr. .6320
LS = 3.8747^2 + 25(.6320)^2 = 24.99999
looks promising.
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