how to fin dalta from this equation

 how to solve this equation attached to file

[KALYAN ACHARJYA]

Good Question

x+c1cosx=c2 solve for x?

where c1, c2 constant.

Answer 1

[David Goodmanson]

Hello Hussein,

A plot of the equation shows that there are three real roots:

x = -2:.001:6;
figure(1)
y = x + 1.6*cos(x)-1.303;
plot(x,y)

Of the many ways to find the roots, just for fun the method below finds a new x value from the present value and iterates. One could keep track of progress and stop after a certain tolerance was reached, but this method is so fast that it's easier to run the for loop a lot of times and verify the accuracy after that. For this root, you can guess basically anything for the starting value of x.

The final result shows 0 for the imaginary part so taking x = real(x) is justified.

You can see that their value of 2.08 is not very good, although it's possible that they were carrying more significant figures than they showed on their next-to-last-line.

format long
x = 4;              % starting point
for k = 1:400
  x = acos((1.303-x)/1.6);
end
x
x = real(x);
accuracy_check = x+1.6*cos(x)-1.303

x = 2.072569688766171 - 0.000000000000000i
accuracy_check = 2.220446049250313e-16

If you want to obtain the other two roots then you would iterate on

x = 1.303-1.6*cos(x);

in which case the initial value for x determines which root you get.