Question

I will give a medal, PLEASE HELP ME!

I understand part one and part two, but I am having trouble with the third part asking if the graphs are the same and to explain my answer:

Show that the solution of dy/dx = - (1+y^2)/(1+x^2) when y(0) = -1
is tan inverse (x) + tan inverse (y) = - pi/4

AND

Show that tan inverse (x) + tan Inverse (y) = -pi/4 can be written as :
y = (x+1)/(x-1)

So my problem is this third part -

are the graphs of tan inverse (x) +tan inverse (y) = -pi/4 AND y=(x+1)/(x-1) the same?? EXPLAIN YOUR ANSWER....PLEASE HELP! Thanks!

Answer 1

I wrote
\[ \tan^{-1} x + \tan^{-1} y = -\frac{\pi}{4} \\
\tan^{-1} y = - \tan^{-1} x - \frac{\pi}{4} \\
y = \tan \left( - \tan^{-1} x - \frac{\pi}{4} \right)
\]
and plotted both curves.

Answer 2

They look the same

Answer 3

Do you think that is a good enough explanation, I mean I would think so, my teacher grades so stinkin hard...Everyone is failing :(

Answer 4

I hope so. Please post here how it goes... I am curious if there is something more they want.

Answer 5

WHy does my graphing calculator show the graphs are different? Just curious if I am doing something wrong :)

Answer 6

what is the difference?

Answer 7

It shows graphs in the 2nd and 4th quadrant as well

Answer 8

open study keeps kicking me off, so I am trying to stay with you, fyi...sorry if Im not here when ever you get back to me. THANKS!!

Answer 9

I figured it out, thanks so much for the help!