(adsbygoogle = window.adsbygoogle || []).push({}); 1. The position vector of a particle at time t ≥ 0 is given by r = sin(t)*i + cos(2t)*j. Find the cartesian equation for the path of the particle.

2. I was told that the answer is:

y = 1 - 2x^2

But I don't know how to obtain that solution.

3. r = sin(t)*i + cos(2t)*j

At first I thought I would merely plug in the values:

x = i, y = j and √(x^2 + y^2) = r, but that wasn't working out:

√(x^2 + y^2) = x sin(t) + y cos(2t)

x^2 + y^2 = x^2(sin(t))^2 + 2xysin(t)cos(2t) + y^2(cos(2t))^2

Solve with CAS Calculator:

t = -pi/2

Substitute that back in:

x^2 + y^2 = x^2(-1)^2 + 2xy(-1)(0) + y^2(-1)^2

x^2 + y^2 = x^2 + y^2

0 = 0

Now I am lost. Please help me!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Converting Position Vector vs Time to Cartesian Coordinates

**Physics Forums | Science Articles, Homework Help, Discussion**