Question

Graph each pair of parametric equations.

1.x = 3 sin3t
y = 3 cos3t

Answer 1

square them and add

Answer 2

x² = 9sin² 3t
y² = 9cos² 3t

Answer 3

x² + y² = 9sin² 3t + 9cos² 3t = 9(sin² 3t + cos² 3t)

Answer 4

yess, next use the identity : \(\sin^2 \theta + \cos^2 \theta = 1\)

Answer 5

sin² 3t + cos² 3t = 1, so...
x² + y² = 9

Answer 6

yes, does that look familiar to u ?

Answer 7

yess

Answer 8

draw it :)

Answer 9

so now i graph

Answer 10

yes, just draw it, and after that u can figure out the direction

Answer 11

i think i need help is it graphed as a circle

Answer 12

you're right ! \(x^2+ y^2 = r^2\) is an equation of circle wid radius \(r\) and center at origin

Answer 13

thank you!

Answer 14

wat about the direction ?
when u graph a parametric curve, u must specify direction also :)

Answer 15

x = 3 sin3t
y = 3 cos3t

when t = 0, x = 0, y = 3
when t = pi/6, x = 3, y = 0