Thread: Parametric Equations to Rectangular Equation

Find the rectangular equation of the curve:
the parametric curve x = 2 sin(t), y = 2 cos(t).

I know it is a circle, centered at the origin, with radius of 2. But, since it goes clockwise, instead of counterclockwise like circles normally do, I can't figure out the rectangular equation.

Originally Posted by kiddopop

Find the rectangular equation of the curve:
the parametric curve x = 2 sin(t), y = 2 cos(t).

I know it is a circle, centered at the origin, with radius of 2. But, since it goes clockwise, instead of counterclockwise like circles normally do, I can't figure out the rectangular equation.

square both equations ...

$\displaystyle x^2 = 4\sin^2{t}$

$\displaystyle y^2 = 4\cos^2{t}$

-------------------- add em' up

$\displaystyle x^2 + y^2 = \, ?$

x^2 + y^2 = 4 sin^2(t) + 4 cos^2(t)? How is that right? I thought that when you change parametric equations to a rectangular equation you get rid of the "t's."

Originally Posted by kiddopop

x^2 + y^2 = 4 sin^2(t) + 4 cos^2(t)? How is that right? I thought that when you change parametric equations to a rectangular equation you get rid of the "t's."

you did not finish it ...

what does $\displaystyle 4\sin^2{t} + 4\cos^2{t} = 4(\sin^2{t}+\cos^2{t}) = \,?$

Ohhhhh. I didn't even think of that. Sorry. Thanks for the help!