Question

Eliminate the parameter.
x = 4 cos t, y = 4 sin t

Answer 1

\(\cos^2t+\sin^2t=1\) Right?

Answer 2

Yeah

Answer 3

OK, so for example, if I had:
x = r cos t, y = r sin t

then, I would eliminate the parameters like this:
\(x^2+y^2=(r \cos t)^2+(r\sin t)^2\)
\(x^2+y^2=r^2\cos^2t+r^2\sin^2t\)
\(x^2+y^2=r^2(\cos^2t+\sin^2t)\)
\(x^2+y^2=r^2\)

Answer 4

Oh, wow. That makes sense. Thanks for the help!

Answer 5

So, you know that \(y=r\sin t\) and \(x=r\cos t\) just give the equation of a circle with radius of \(r\), and centered at the origin.

Answer 6

So, your answer would be (if you don't mind) ?

Answer 7

\[\cos t=\frac{ x }{ 4 },\sin t=\frac{ y }{ 4 }\]
\[\cos ^2t+\sin ^2t=1\]