Question

find the approximate equation of the line tangent to the graph of y=xcscx at x=pi/6

Answer 1

@jdoe0001 if you could help i would appreciate it

Answer 2

You need to differentiate y

Answer 3

yes i get it to be -cscxtanx+cscx

Answer 4

where this tan come in?

Answer 5

\[y'=(x)'\csc(x)+x(\csc(x))' \\ y'=1 \csc(x)+x(-\csc(x)\cot(x))\]

Answer 6

yes thats correct and then i plug in pi/6 and end up with -1.4641

Answer 7

now you plug in pi/6 to get the slope of the line

Answer 8

which is not one of my anwser choices

Answer 9

csc(pi/6)=2
and cot(pi/6)=sqrt(3)

Answer 10

\[y'|_{x=\frac{\pi}{6}}=2-\frac{\pi}{6} (2)(\sqrt{3})=2-\frac{\sqrt{3} \pi}{3}\]

Answer 11

and yes that gives me a totally different slope number than what you got

Answer 12

approximately .1862

Answer 13

yes thats correct also i realized my mistake thank your for your time and effort as i appreciate your assistance @freckles

Answer 14

np