Question

11. The slope of normal of y= sin x at x=0 is
a. 0
b. -1
C. 1
d. not defined​

Answer 1

$0$

Step by step

Answer:

The equation of normal is y=-x.

Step-by-step explanation:

The equation of curve is

$y=\sin \: xy=sinx$

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.