# What is the equation of the line normal to # f(x)=xsin(3x+pi/4)# at # x=pi/2#?

##### 1 Answer

Feb 4, 2017

#### Explanation:

graph{(xsin(3x+.7854)-y)(0.3809x+y+0.5124)=0 [-40, 40, -20, 20]}

Uniform scale graphs.

graph{(xsin(3x+.7854)-y)(0.38x+y0.51)((x-1.5804)^2+(y+1.1107)^2-.01)=0 [0, 2, --100, 100]}

with zeros at x = 1/3(k-1/4)pi. k = 0, +-1, +-2, ... that have common

spacing

The foot of the normal is

Slope of the normal =

So, the equation to the normal at P is