# Finding solution of a complex trig equation

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Naveen Ramesh on 29 Apr 2013
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.. !!

Walter Roberson on 29 Apr 2013
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.