Question

please solve this...open complete image

Answer 1

y=3 sint-sin³t
dy/dt=3cost-3sin²tcost=3cost(1-sin²t)=3costcos²t=3cos³t


x=3cost-cos³t
dx/dt=-3sint-3cos²tsint=3sint(1-cos²t)=3sintsin²t=3sin³t
dy/dx=(dy/dt)/(dx/dt)
=3cos³t/3sin³t=cot³t
slope of normal=-1/dy/dx=-1/cot³t=-tan³t