Position vector of a particle moving in xy plane at time t is r→=a(1−cos⁡ωt)i^+asin⁡ωtj^ . The path of the particle is

Particle is moving in a circle of radius a and center (a, 0) with constant angular velocity ω. At time t=0 particle is at origin and it starts r = rotating clockwise. At time r it hasrotated an angle θ given by: θ=ωty=asin⁡θ=asin⁡ωt and x=a−acos⁡θ=a(1−cos⁡ωt)∴ r→=a(1−cos⁡ωt)i^+asin⁡ωtj^