Consider the parametric equations

x=cos t - sin t y=cos t + sin t
0

Question

Consider the parametric equations 

x=cos t - sin t       y=cos t + sin t
0<or equal t<or equal 2pi

a)Eliminate the parameter t to find the Cartesian equation for the parametric curve
b)Sketch the curve indicating with arrows the direction in which the curve is traced

amistre64 · Answer

well, it might be helpful to know that r^2 = x^2+y^2

other than that its hard to see pulling out a t at the moment

amistre64 · Answer

what ideas have you tried so far?

amistre64 · Answer

as far as plotting goes, its a circle ...

sirm3d · Answer

add and subtract the two equations:
$$x+y=2\cos t\y-x=2\sin t$$

sirm3d · Answer

square both equations, add them, and use a trigonometric identity.

amistre64 · Answer

x = cos t - sin t  ; y = cos t + sin t 

x^2 = cos^2 t -2sin t cos t + sin^2 t
y^2 = cos^2 t +2sin t cos t + sin^2 t
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r^2 = 2(cos^2 t + sin^2 t) = 2

x^2 + y^2 = 2

amistre64 · Answer

yeah, thats what i kept coming up with :)  didnt know if the question needed a function tho