Question

The equation to the normal to the curve $y = \sin x$ at (0, 0) is

• A. $x = 0$
• B. $y = 0$
• C. $x + y = 0$
• D. $x - y = 0.$

Answer 1

Answer: (C)

$y = sin\,x$
$\Rightarrow \frac{dy}{dx} = cos\,x$
At $\left(0,0\right), \frac{dy}{dx} = cos\,0=1$
$\therefore $ slope of the normal $= \frac{1}{-1} = -1$
$\therefore $ normal at $\left(0, 0\right)$ is
$y - 0 = - 1\left(x - 0\right) = - x$ i.e., $x + y = 0$