# From Scientific Calculator [Solve] to matlab

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Alex on 24 Oct 2017
Commented: Torsten on 24 Oct 2017
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

Mischa Kim on 24 Oct 2017
Edited: Mischa Kim on 24 Oct 2017
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.

Torsten on 24 Oct 2017
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.

Alex on 24 Oct 2017
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

#### 1 Comment

Torsten on 24 Oct 2017
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.

Steven Lord on 24 Oct 2017
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.