From Scientific Calculator [Solve] to matlab

Hi all, with my scientific calculator I could try something as the following

SHIFT+CLR(9)  >> (3)>>Reset All >>[=] Reset All >> Press [AC]
-Set the calculator on the right limits:

       sin(30)=1/2
       sin(x) = 1/2 and solve for x  [SHIFT] [SOLVE] [=] = 30
  or 

cos(X)^2*cos(3X)^2 = 0.5 and then SHIFT>>SOLVE

How I can implement something like that in matlab (especially for the second function at the bottom? How I can implement this solve functionality in matlab? I would like to thank you in advance for your help

Answer 1

[Mischa Kim]

Alex, use something like

 fun = @(X) cos(X)^2*cos(3*X)^2 - 0.5;
 options = optimoptions('fsolve','Display','none','PlotFcn',@optimplotfirstorderopt);
 sol = fsolve(fun,0,options)

The options command is not required but shows you some of the capabilities of MATLAB.

Answer 2

[Torsten]

syms x
eqn = cos(x)^2*cos(3*x)^2-0.5 == 0;
sol = solve(eqn)

or

syms x
eqn = cos(x)^2*cos(3*x)^2-0.5 == 0;
sol = vpasolve(eqn)

Best wishes

Torsten.

Answer 3

[Alex]

Thanks a lot for all the replies. Unfortunately both suggestions

syms x
eqn = cos(x)*cos(3*x)-0.5707 == 0;

sol = vpasolve(eqn)

fun = @(X) cos(X)*cos(3*X) - 0.5707;
 options = optimoptions('fsolve','Display','none','PlotFcn',@optimplotfirstorderopt);
 sol = fsolve(fun,0)

do not return any solution, even though I simplified the equation. At the same time the calculator is spot on. What is the extra level of details that are required from matlab in this regard?

Thanks a lot Alex

[Torsten]

Maybe you neither have the symbolic toolbox nor the optimization toolbox installed ?

Does

x0 = 0;
fun = @(X) cos(X)*cos(3*X) - 0.5707;
sol = fzero(fun,x0)

work ?

Best wishes

Torsten.

Answer 4

[Steven Lord]

Since this is one equation in one unknown, you can use fzero to solve this.

>> f = @(x) cos(x)*cos(3*x)-0.5707;
>> result = fzero(f, 0);
>> check = f(result)
check =
     0

However, it appears your calculator computes the cosine of angles in degrees. The cos function in MATLAB computes the cosine of an angle in radians. To compute the cosine of an angle in degrees in MATLAB, use the cosd function instead of cos.