SOLUTION: Graph each pair of parametric equations. (2 points each) x = 3 sin3t y = 3 cos3t

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Question 1137289: Graph each pair of parametric equations.
(2 points each)
x = 3 sin3t
y = 3 cos3t

Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52847) About Me  (Show Source):
You can put this solution on YOUR website!
.

Circle of the radius of 3 units, centered at the origin of the (x,y) coordinate plane.

When " t " changes from 0 to 2pi radians, the point (x,y) makes precisely three full rotations clockwise
along the circle, starting from the position 12:00 ( 3 units vertically up, or (0,3) ).


Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Square the expressions for both x and y and then use the Pythagorean identity

sin%28x%29%5E2%2Bcos%28x%29%5E2+=+1

x%5E2+=+9sin%5E2%283t%29
y%5E2+=+9cos%5E2%283t%29
x%5E2%2By%5E2+=+9%28sin%5E2%283t%29%2Bcos%5E2%283t%29%29+=+9%281%29+=+9

The equation is

x%5E2%2By%5E2+=+9

which you surely know is a circle with center at the origin and radius 3.