Question

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

Answer 1

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Answer 2

Answer:

The equation of normal is y=-x.

Step-by-step explanation:

The equation of curve is

$y=\sin x$

Differential with respect to x.

$\frac{dy}{dx}=\cos x$

$\frac{dy}{dx}_{(0,0)}=\cos (0)=1$

The slope of normal is

$m=\frac{-1}{\frac{dy}{dx}_{(0,0)}}=\frac{-1}{1}=-1$

The slope of normal at (0,0) is -1. The equation of normal is

$y-y_1=m(x-x_1)$

$y-0=-1(x-0)$

$y=-x$

Therefore the equation of normal is y=-x.