Calculating tangent angle of an elipse

[jbhiker]

I have scoured this board for an answer. I wish to calculate the angle of the tangent of any point along an elipse. Creating the elipse was easy thanks to your assistance. I found a post with a formula to plot the X,Y coordinates of each point of an elipse using this formula and creating polar coordinates and 170 points on the elipse:

1		H=5		Input C1 for half-height on the Y-Axis(vert)
2		W=15		Input C2 for half-width on the X-Axis (horiz)
3				This line is blank intrentionally
4	A	X	Y	Notes on the formula
5	0	15.000	0.000	// B5 and down: =(ROWS(B$5:B5) - 2)/(ROWS(B$5:B$175) - 1) * 360
6	2.117	14.990	0.184	// C5 and down: =D$2*COS(RADIANS($B5))
7	4.235	14.959	0.369	// D5 and down: =D$1*SIN(RADIANS($B5))

<colgroup><col span="2"><col><col><col></colgroup><tbody>
</tbody>

In this formula, the angle A is calculated from the center of the elipse. I need it to be a tangent to the elipse and thought I could do it using the TAN function but I am missing something. Any comments would be appreciated greatly.
Thank you for your time

 

[patel45]

geometry - Calculating a Point that lies on an Ellipse given an Angle - Mathematics

 

[shg]

       -----A----- --B-- -C-- ---D---
   1   Half Height h        5        
   2   Half Width  w       15        
   3                                 
   4        A        X    Y    Slope 
   5             0 15.00 0.00 #DIV/0!
   6            30 12.99 2.50   -0.58
   7            45 10.61 3.54   -0.33
   8            60  7.50 4.33   -0.19
   9            90  0.00 5.00    0.00
  10           120 -7.50 4.33    0.19

The formula in D5 and copied down is

=-h / (w * TAN(RADIANS(A5)))

 

[jbhiker]

-----A----- --B-- -C-- ---D---
1 Half Height h 5
2 Half Width w 15
3
4 A X Y Slope
5 0 15.00 0.00 #DIV/0!
6 30 12.99 2.50 -0.58
7 45 10.61 3.54 -0.33
8 60 7.50 4.33 -0.19
9 90 0.00 5.00 0.00
10 120 -7.50 4.33 0.19

The formula in D5 and copied down is

=-h / (w * TAN(RADIANS(A5)))

>>>>>>>>>>>>>>>>>>>
Hmmmm... I am not sure that will give me the answer I was looking for.
That formula gives me the slope of the X,Y coordinates.
But I do not see yet what that number means.
I am not sure how I can derive the angle of the tangent from those results
Can you explain?
The result I am looking for will be an eliptical starburst if a line is drawn at the derived angle from each point "X,Y".
Thanks in advance!

 

[jbhiker]

Couldn't I just calculate the angle between 2 points (Xa,Ya) and Xb,Yb), add 90 degrees and have my answer?
That is what I am trying to do now. I am also trying to understand your answer which is probably the same thing - it is just going over my head.
JB

 

[shg]

The answer gives the slope. If you want the angle, take the inverse tangent of the slope and convert to degrees, e.g., in E5 and copy down

=degrees(atan(e5))

 

[shg]

Edit: The slope of a line is the rise over the run (the change in y divided by the change in x).

 

[jbhiker]

Now I get it... awesome! Just a little knowledge puts a large number of things into perspective.
Thank you so much SHG. Clearly you paid more attention in your Trig class than I did.
JBHiker - Texan at large in California

 

[shg]

You're welcome, good luck.