A particle moves in x-y plane according to rule x = a sin ωt and y = a cosωt. What kind of path does the particle follow ?

(1) An elliptical path
(2) A circular path
(3) A parabolic path
(4) A straight line path inclined equally to x and y axes.

1 Answer
Apr 23, 2018

(2) A circular path.

Explanation:

As x=asinomegat and y=acosomegat

sinomegat=x/a and cosomegat=y/a

Hence squaring and adding

sin^2omegat+cos^2omegat=x^2/a^2+y^2/a^2

or x^2/a^2+y^2/a^2=1

or x^2+y^2=a^2

Hence, it is (2) A circular path.