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. $x-y=0$
Solution:
Given that $y=\sin x$
Slope of the tangent $\frac{d y}{d x}=\cos x$
Slope at origin $=\cos 0=1$
Equation of normal:
$\left(y-y_{1}\right)=\frac{-1}{\text { Slope of tangent }}\left(x-x_{1}\right)$
$\Rightarrow(\mathrm{y}-0)=\frac{-1}{1}(\mathrm{x}-0)$
$\Rightarrow \mathrm{y}+\mathrm{x}=0$
$\Rightarrow y+x=0$
Hence option C is correct.