# tan and atan quadrants and graph - Nahin an Imaginary TaleWatch

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#1
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
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1 week ago
#2
(Original post by veekm)
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)
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#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
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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.
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