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

Answer: (B)

$x = 1$

Answer 2

$y = \sin\frac{\pi x}{2}$ ⇒ $\frac{dy}{dx} = \frac{\pi}{2}\cos\frac{\pi}{2}x$ ⇒ $\left( \frac{dy}{dx} \right)_{(1,1)} = 0$

$\therefore$ Equation of normal is $y - 1 = \frac{1}{0}(x - 1)$ ⇒ $x = 1$