2

$x = 2 \cos t$, $y = 2 \sin t$, $0 \le t \le 2\pi$

Find the Cartesian equation of the curves.

Please help i know it's basic but my problem is that $2 \cos t$ doesn't equal $1 - \sin^2 t$ and if it does how? (maybe i just need a re-freshener).

Help would be greatly appreciated! thank you.

Mahdi Khosravi
  • 3,989
MATHSUSER
  • 391
  • Tell me which famous formula do you know that includes the basic functions $\sin t,\cos t$? – Mikasa Jul 19 '13 at 07:37

1 Answers1

1

$$x=2\cos t,y=2\sin t$$ $$\cos t=\dfrac x2,\sin t=\dfrac y2$$ since $$\cos^2t+\sin ^2t=1$$ so $$\left(\dfrac x2\right)^2+\left(\dfrac y2\right)^2=1$$ $$x^2+y^2=4$$ this is equation of a circle having centre ($0,0$) and radius= $2$

iostream007
  • 4,529