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**1. The question**

The position of a particle is given by r(t) = acos(wt) i + bsin(wt) j. Assume a and b are both positive and a > b. The plane polar coordinates of a particle at a time t equal to 1/8 of the time period T will be given by _

## Homework Equations

r(t) = acos(wt) i + bsin(wt) j.

## The Attempt at a Solution

at t = T/8 the value of wt=π/4.

therefore in Cartesian coordinates the vector is r= a/√2 + b/√2.

so in polar coordinates this transforms to r = √(a

^{2}+ b

^{2})/2 and tanθ = b/a. My answer does not match with the given one. Also if we were to write the polar equation of the curve how would that follow ?