vpasolve for numerical solution

Hello I am trying to find a solution to the equation:

1= 0.95*2*invtan(4.5/2*r)*r/(4.5)

for the unknown r that satisfies the equality or comes as close to it as possible

I have tried using vpasolve by entering this into matlab:

syms r
vpasolve(0.95 * 2 * atan((4.5)/(2*r)) * r / (4.5) == 1,r)

but I come up with matlab saying

[ empty sum ]

I want to use matlab to solve this, can anyone help?

Answer 1

[Mischa Kim]

Richard, it seems the equation you posted cannot be satisfied.

 0.95 * 2 * atan((4.5)/(2*r)) * r / (4.5) == 1

or

 0.95 * 2 * atan((4.5)/(2*r)) * r / (4.5) - 1 == 0

which I am calling f in the following.

 r = -300:0.1:300;
 f = 0.95*2*atan((4.5)./(2*r)).*r/4.5 - 1;
 plot(r,f)

In other words, there is no r for which f = 0.