Question

Write the equation of the normal to the curve y = cos x at (0, 1).

Answer 1

$$\begin{gathered} \mathrm{Given}: \\ y=\cos x \\ \mathrm{On}\mathrm{d}\text{ifferentiating both sides w.r.t.}x,\mathrm{we}\mathrm{get} \\ \frac{dy}{dx}=-\sin x \\ \mathrm{Now}, \\ \text{Slope of the tangent=}{\left(\frac{dy}{dx}\right)}_{\left(0,1\right)}\text{=-sin 0=0} \\ \mathrm{and} \\ \text{Equation of the normal} \\ =y-y_1=\frac{-1}{m}\left(x-x_1\right) \\ \Rightarrow y-1=\frac{-1}{0}\left(x-0\right) \\ \Rightarrow x=0 \end{gathered}$$