Question

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

Answer 1

$y=\cos x$ at $(0,1)$

To find normal we have to find slope of that normal at $(0,1)$

$y^{\prime }=-\sin x$

$m_{normal}={\frac{1}{\sin x}|}_{x=0}=\infty$

$\therefore$ Equation of normal

$\Rightarrow (y-1)=m_{normal}(x-0)$

Since $m_{normal}$ is infinity.

Equation of normal is $x=0$.