Question

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

• A. y =1
• B. x =1
• C. y =x
• D. $y-1=\frac{-2}{\pi }(x-1)$

Answer 1

The correct option is B x =1

$y=sin\frac{\pi x}{2}\Rightarrow \frac{dy}{dx}=\frac{\pi }{2}cos\frac{\pi }{2}x\Rightarrow {\left(\frac{dy}{dx}\right)}_{(1,1)}=0$
$\therefore$ Equation of normal is $y-1=\frac{1}{0}(x-1)$
$\Rightarrow x=1$.