A particle is moving in XY-plane such that x=b(2t+sin⁡2t),y=b(1−cos⁡2t)

(1) ∵x=b(2t+sin⁡2t)or vx=dxdt=2b+2bcos⁡2tor ax=dvdt=−4bsin⁡2t∵y=b(1−cos⁡2t)or vy=2bsin⁡2tor ay=dvydt=4bcos⁡2t∴a=ax2+ay2=4b(3) tan⁡θ=vyvx=2bsin⁡2t2b+2bcos⁡2t=sin 2t2 cos2 t=2 sin t cos t2 cos2 t=tan t At t=π4, θ=π4