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

x = 0 y = 0 x + y = 0 x - y = 0

x + y = 0

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