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

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

Application of Derivatives

Solution:

Since $\frac{dy}{dx} = cos\,x$,
therefore, slope of tangent at $\left(0,0\right) = cos\, 0 = 1$ and hence slope of normal at $\left(0,0\right)$ is $- 1$.
$\therefore $ Equation of normal is $y-0 = - 1 \left(x-0\right)$
$\Rightarrow x + y = 0$