Solve Parametric Equation for Motion of Particle XY

[evilpostingmong]

Homework Statement

Describe motion of a particle w/ position xy

Homework Equations

x=cospi(t) y=sinpi(t)

The Attempt at a Solution

solving for t
t=x/cospi
so y=sinpi(x)/cospi
y=tanpi(x)

interval=at least one at most 2
since tan(x)=0 at pi and 2pi
and this is where the boundaries are so the particle travels from pi and 2pi counterclockwise
but the textbook has a different (but reasonable) answer in that it squares cos pi and
sin pi to equal 1 and uses the circle equation but ends up with the same diagram and
direction. If I went wrong, can you please tell me where I went wrong since my answer
seems legit to me.

 

[Vagrant]

x= cos\pit
should become
t=cos^{-1}x/\pi

 

[tiny-tim]

have some π …

x=cospi(t) y=sinpi(t)
…
If I went wrong, can you please tell me where I went wrong since my answer
seems legit to me.

Hi evilpostingmong!

Your initial equations are wrong.

It isn't x=cosπ(t) y=sinπ(t);

it's x=cos(πt) y=sin(πt).

Now try!

(oh … and here's some π and other things to pack in your bag …)