Question

Find the slope of tangent of the curve$x=a{\sin }^{3}t,y=b{\cos }^{3}t$ at $t=\frac{\pi }{2}$

• A. $cott$
• B. $-tant$
• C. $-cott$
• D. $\text{not defined at}$ $\frac{\pi }{2}$

Answer 1

The correct option is D $\text{not defined at}$ $\frac{\pi }{2}$

$x=asi{n}^{3}t$

$dx=a3si{n}^{2}t\left(cost\right)dt$…(1)

$y=bco{s}^{3}t$

$dy=b3co{s}^{2}t(-sint)dt$ ..(2)

At $t=\frac{\Pi }{2}$

$\frac{dx}{dt}=0$ and hence $\frac{dy}{dx}=\text{not defined}$