SOLUTION: Hi, There's a parametric equations problem I'm confused about. The question is: convert this set of parametric equations to rectangular form - x = 3cos(t) and y = 3sin(t). I kn

Algebra ->  Systems-of-equations -> SOLUTION: Hi, There's a parametric equations problem I'm confused about. The question is: convert this set of parametric equations to rectangular form - x = 3cos(t) and y = 3sin(t). I kn      Log On


   

Question 1181001: Hi,
There's a parametric equations problem I'm confused about. The question is: convert this set of parametric equations to rectangular form - x = 3cos(t) and y = 3sin(t). I know that the trig identity x^2 + y^2 = 1 is involved here but I'm not sure how.
Thank you for your help!
Answer by ikleyn(52903) About Me  (Show Source):
You can put this solution on YOUR website!
.

If your parametric equations are

    x = 3cos(t)

    y = 3sin(t),


then SQUARE each equation and then add them.


You will get


    x^2 + y^2 = 9cos^(t) + 9sin^2(t) = 9*(sin^2(t) + cos^2(t)) = 9.


So, you just converted the given parametric equations to rectangular form
and this converted (resulting) equation is


    x^2 + y^2 = 9.


It is the standard equation of the circle  of the radius of 3 units centered at the origin of the coordinate system.


    +--------------------------------------------------------+
    |  CONGRATULATIONS :  you just completed the solution    |
    |        and reached your destination (!)                |
    +--------------------------------------------------------+

Solved, answered, carefully explained and completed.