r1=(cos(t))i+(sin(t))j r2 = (cos(2t))i+(sin(2t))j
Show that these particles have the same path. I need help showing that they have identical Cartesian equation... but I cannot remember how to do this. Please help

Question

r1=(cos(t))i+(sin(t))j  r2 = (cos(2t))i+(sin(2t))j
Show that these particles have the same path.  I need help showing that they have identical Cartesian equation... but I cannot remember how to do this.  Please help

anonymous · Answer

@ganeshie8 @agent0smith can either of you help?

anonymous · Answer

I am getting confused by the unit vectors I think.

anonymous · Answer

so, do i just figure out the x and y components separately... so r=cos t and r=sin t?

agent0smith · Answer

Convert from polar to rectangular coordinates i think.

like the first
x=cost
y=sint

r^2 = x^2 + y^2

If you do the same for the second, it'll be cos^2 2t + sin^2 2t  which equals 1, just like the first

anonymous · Answer

sweet.  I have been looking at this for an hour.  thanks for clarifying.  all the examples in the book are in the 2Dimension section.. so none deal with vectors.  thanks again very much