Optimization problem for trigonometric functions

How to minimize below equation wrt θ (Theta) where k, l0, cotθ0, r1 and r2 constant only variable is theta

Answer 1

[ANKUR KUMAR]

If k, lo, r1, and r2 are constants, you can use anonymous function to calculate the expression:

k=randi(10,1,1);
lo=randi(10,1,1);
r1=randi(10,1,1);
r2=randi(10,1,1);

% theta in degree
func = @(theta) (k*lo*cotd(theta)/r1^4)+(k*lo*((cscd(theta)/r2^4)-(cotd(theta)/r1^4)))
func(25)  % make sure to put values in degree, not in radians

You can write multiple values while calling the function

func([25,45,120,160])

Answer 2

[David Hill]

I learned that you take the derivative of the function and set it to zero to find the points of relative minimum and maximum.

theta=acos((r2/r1)^4);%after simplifying