Question

help please :(((( supposed to find cartesian equation for x = sin t and y = cos^2 t ... in the range -2pi 10 years ago

Answer 1

x = sin t
y = cos^2 t

x^2 + y = ?

Answer 2

1

Answer 3

Now I do understand that equation and when I try to plot points on my graph I end up with a semi circle in quadrant 1 and 2 along the x-axis, but I don't understand what the behavior would be if it's a semi circle, would a particle only be traveling along the half circle from -1 to 1 and then make another loop ? or is the direction assuming two passes along the semi circle.?

Answer 4

do you really think \(x^2+y=1\) is a circle ?

Answer 5

no, but Im confused because the range is supposed to be from -2pi to 2pi?

Answer 6

Maybe forget about range for now
what do you know about the graph of \(x^2+y=1\) ?

Answer 7

that x^2 is a parabola and y would be a horizontal shift

Answer 8

right, try sketching the graph

Answer 9

Got it. Thank you

Answer 10

what about range ?

Answer 11

if it helps, split the given range of \(t\) into multiple intervals like :

(0, pi/2)
(pi/2, pi)
(pi, 3pi/2)
(3pi/2, 2pi)

and see what part of the graph gets traced in each interval

Answer 12

I'm sorry to bother you but I am still having a bit of trouble, I thought I figured it out, but Im still stuck. :(