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

We have,

$y=\sin x \Rightarrow \frac{d y}{d x}=\cos x \Rightarrow\left(\frac{d y}{d x}\right)_{(0,0)}=\cos 0=1$

So, the equation of the normal at (0, 0), is

$y-0=-\frac{1}{1}(x-0) \Rightarrow y+x=0$