tan and atan quadrants and graph - Nahin an Imaginary Tale Watch

veekm
Badges: 8
Rep:
?
#1
Report Thread starter 1 week ago
#1
Name:  nahin.png
Views: 2
Size:  162.2 KB So if you look at that image - I've written down the Questions in the image.
1. how do we get the atan graph?
2. why does Nahin say that complex numbers exist in the 4,2 quadrants? Theta = atan(b/a) will exist only in 1,3 quadrants by the look of that graph.. so..

could someone elucidate..
(also if someone wants to team up and tackle this book - we could try together and swap notes) I'm trying to figure out complex math and read Daniel Fleisch Waves book and e^1Theta + sin behavior needs to be understood.
Last edited by veekm; 1 week ago
0
reply
mqb2766
Badges: 17
Rep:
?
#2
Report 1 week ago
#2
(Original post by veekm)
Name:  nahin.png
Views: 2
Size:  162.2 KB So if you look at that image - I've written down the Questions in the image.
1. how do we get the atan graph?
2. why does Nahin say that complex numbers exist in the 4,2 quadrants? Theta = atan(b/a) will exist only in 1,3 quadrants by the look of that graph.. so..

could someone elucidate..
(also if someone wants to team up and tackle this book - we could try together and swap notes) I'm trying to figure out complex math and read Daniel Fleisch Waves book and e^1Theta + sin behavior needs to be understood.
The atan isn't too difficult. If (x,y) describe the forwards relationship tan then (y,x) represents atan.
When a<0, then you're in Q2 or 3. When b<0, it's Q3 or 4.
That's about all there is to it. The ratio b/a obviously looses some sign info, compared to the pair(a,b)
0
reply
veekm
Badges: 8
Rep:
?
#3
Report Thread starter 1 week ago
#3
thanks..

regarding the atan - I figured a better way to visualize.. if points are closer to the x-axis, then when you interchange the axis, the points get dragged towards the erstwhile 'y' so the graph looks flipped around the diagonal..

regarding a<0, the curve doesn't exist in some quadrants so I guess he's plain wrong imho - till I figure that out to my satisfaction
0
reply
mqb2766
Badges: 17
Rep:
?
#4
Report 1 week ago
#4
(Original post by veekm)
thanks..

regarding the atan - I figured a better way to visualize.. if points are closer to the x-axis, then when you interchange the axis, the points get dragged towards the erstwhile 'y' so the graph looks flipped around the diagonal..

regarding a<0, the curve doesn't exist in some quadrants so I guess he's plain wrong imho - till I figure that out to my satisfaction
When you consider -pi/2 .. pi/2 you're only considering half the angles. Its easy to add the other parts to get -pi .. pi onto both the tan and atan curves which means the other quadrants are visited.
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • University of Hertfordshire
    All Subjects Undergraduate
    Sat, 22 Feb '20
  • Ravensbourne University London
    Undergraduate Open Day Undergraduate
    Sat, 22 Feb '20
  • Sheffield Hallam University
    Get into Teaching in South Yorkshire Undergraduate
    Wed, 26 Feb '20

People at uni: do initiations (like heavy drinking) put you off joining sports societies?

Yes (415)
67.37%
No (201)
32.63%

Watched Threads

View All