Question

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

Answer 1

\[\text { Given }: \]

\[y = \cos x\]

\[\text { On differentiating both sides w.r.t.x, we get }\]

\[\frac{dy}{dx} = - \sin x\]

\[\text { Now }, \]

\[\text { Slope of the tangent }= \left( \frac{dy}{dx} \right)_\left( 0, 1 \right) =-sin 0=0\]

\[\text { and }\]

\[\text { Equation of the normal }\]

\[ = y - y_1 = \frac{- 1}{m}\left( x - x_1 \right)\]

\[ \Rightarrow y - 1 = \frac{- 1}{0}\left( x - 0 \right)\]

\[ \Rightarrow x = 0\]