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. $y-1=\frac{-1}{\pi }(x-1)$

Answer 1

The correct option is B x = 1

$y=sin\frac{\pi x}{2}\Rightarrow \frac{dy}{dx}=\frac{\pi }{2}\cdot \cos \frac{\pi x}{2}\Rightarrow {\frac{dy}{dx}|}_{(x,y)=(1,1)}=0\therefore \text{Slope of normal}=\infty \therefore \text{Normal is}\parallel \text{to Y-axis}\therefore \text{Normal is}x=1$