A line is defined by the parametric equations: x = cos2t and #y = sin^2t# how do you find the cartesian equation of the line?

Answer 1

Luke Alvarez

The equation of the line is #2y+x=1#

Use the fact that #cos2t=1-2sin^2t#

#x=cos2t=1-2sin^2t#

Then as #y=sin^2t#

We have to eliminate #sin^2t# between the 2 equations

We finally get

#x=1-2y#

tht is #2y+x=1#

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Answer 2

Isaiah Allen

To find the Cartesian equation of the line defined by the parametric equations (x = \cos^2 t) and (y = \sin^2 t), eliminate the parameter (t) by expressing (t) in terms of (x) and (y), then substitute these expressions into one of the parametric equations. This will give you the Cartesian equation of the line.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.