Finding solution of a complex trig equation

Hi guys, I have this problem wherein there are 3 variables, namely 'beta', 'delta_beta' and 's'. I ll have to plot the graph between s and beta and then between s and delta_beta. And i also need to find the minum value of both. I have this complex trig equation that goes like this,

acos((u/R)*sin(beta + delta_beta)) = asin((s - (u*cos(beta + delta_beta)))/R);

In this equation, u and R are constants and s is defined as

s=0:0.1:35;

I have the values of beta from a previous equation that I also have to input into the above equation to get the values of delta_beta and finally plot it.

The problem that I am facing is that Matlab is not able to solve these equations and hence i am not able to get the plots. I dont know what the problem is and I ll be really grateful if someone could offer me a solution. and as always, thanks a ton.. !!

Answer 1

[Walter Roberson]

Two related solutions:

atan2((-R^4+(2*u^2+2*s^2)*R^2-(s-u)^2*(s+u)^2)^(1/2)/(u*s), (u^2+s^2-R^2)/(u*s))-beta

atan2(-(-R^4+(2*u^2+2*s^2)*R^2-(s-u)^2*(s+u)^2)^(1/2)/(u*s), (u^2+s^2-R^2)/(u*s))-beta

That is, the two first arguments are negatives of each other.