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

The correct option is C $x+y=0$

Given: $y=\sin x$

To find: Eq. of normal to curve at $(0,0)$

Solution: $y=\sin x$

$\frac{dy}{dx}=\cos x$

${\frac{dy}{dx}]}_{(0,0)}=\cos 0=1$

Eq. of normal:

Slope of normal

$=\frac{-1}{\frac{dy}{dx}}=-1$

Eq. of normal at $(0,0)$ $\Rightarrow y-0=-1(x-0)$

$y=-x$

$y+x=0$

$\therefore x+y=0$ is the required.

Eq. of normal to curve $y=\sin x$ at $(0,0)$.