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

Answer 1

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.