The equation of normal to the curve $x=\theta+\sin \theta, y=1+\cos \theta$ at $\theta=\frac{\pi}{2}$ is

The length of the longest interval, in which the function $3 \sin x-4 \sin ^3 x$ is increasing, is

If Rolle's theorem holds for the function $\mathrm{f}(x)=x^3+\mathrm{bx}{ }^2+\mathrm{ax}+5$ on $[1,3]$ with $\mathrm{c}=2+\frac{1}{\sqrt{3}}$, then the values of $a$ and $b$ respectively are

The normal to the curve, $y(x-2)(x-3)=x+6$ at the point, where the curve intersects the Y-axis, passes through the point