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February 21st, 2009, 03:00 PM   #1
Joined: Feb 2009

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Solve angle and radius of oval

I have a formula:
X = (radius*n+f)*sin(a)
Y = radius*cos(a)

Which, when plotted, gives me a very flat oval when the radius is
small moving out to a circle and then to a tall oval. (eg. n = 0.55,
f=195, becomes a circle when the radius is approx 433.333)

Now what I need is to be able to reverse the formula. I have the
values for X, Y, n, f. I need to calculate rad and a.

If I re-arrange the formula to :

X = ((Y/cos(a))*n+f)*sin(a)


X = Y*n*sin(a)/cos(a) + f*sin(a)

All values are known except a.
But how do I re-write this so I have a formula
a = .........
pmoor is offline  
February 21st, 2009, 05:55 PM   #2
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Joined: Dec 2006

Posts: 20,264
Thanks: 1959

You can use sina + cosa = 1 to eliminate a, and then solve the resulting quartic equation for the radius.
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