Homework Help: Parametric to Rectangular?

Posted by Tabby on Sunday, April 22, 2012 at 9:23pm.

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

Parametric to Rectangular? - Reiny, Sunday, April 22, 2012 at 9:39pm
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.

Answer this Question

Related Questions

precalc - What are parametric equations? How would you find the rectangular eq&#...
Pre-Calculus - Find the rectangular equation of the curve whose parametric ...
Trig - Need answer check pls. Find the rectAngular equation for the plane curve ...
calculus - (a) Modifying the parametric equations of a unit circle, find ...
Calc 3 - Find the parametric equations for the tangent line to the curve with ...
Calc 3 - Find the parametric equations for the tangent line to the curve with ...
Calculus - Find parametric equations for the tangent line to the curve with the ...
Math - Eliminate the parameter in the pair of parametric equations to find the ...
Calc. - sketch the curve using the parametric equation to plot the points. use ...
Parametric curves and area - 1.The curve of x=49-t^2 and y=t^3-1*t makes a loop ...

For Further Reading

First Name:
School Subject:
Answer: