troubleshooting Question

x(b) ... a(x,b) ... to give a(x)

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Mike EghtebasFlag for United States of America asked on
Math / Science
9 Comments1 Solution562 ViewsLast Modified:
I have following two equations (r and h are constants):

x=x(b)=r (cos(b)+ tan(b)sin(b)-1)+ tan(b)h                   (eq. 1)
 
a =a(x,b)= (1/r)*sqrt((h + rsin(b))^2 + (x + r - rcos(b))^2) - b-h/r               (eg. 2)    

to make it readable, if we assume S=Sin(b), C=Cos(b), and T=tan(b), then we get:

x=x(b)=r (C+ TS -1)+ Th      <-- these forms may be useful may be not
a =a(x,b)= (1/r)*sqrt((h + rS)^2 + (x + r - rC)^2) - b-h/r;

I want to have the following functions if possible:

a(x)=....?            (eq. 3)
b(x)=....?           (eq. 4)   <-- this one is not that important.      

Question:  Is it possible to find a(x) and b(x) having (eq. 1) and (eq. 4) above?

for background discussions please see: https://www.experts-exchange.com/Programming/Languages/Scripting/Q_27237703.html

Thank you
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