# Not auto change sec(x) to 1/cos(x)?

4 views (last 30 days)
Paul Dostert on 31 Jan 2024
Edited: John D'Errico on 22 Feb 2024
Is there any setting anywhere that prevents symbolic mathematics package from converting sec(x) and csc(x) to their sine/cosine counterparts? Trying to auto-generate a derivative/antiderivative assignment for my calc kids, and they "know" the derivatives/antiderivatives as secs and tans, not necessarily as their sine/cosine equivalents. For example
syms x; sec(x)^2
ans =
I want it to just have sec(x)^2 instead. Any ideas except just converting everything to symbolic (like the trick when you want pi to not be it's numerical equivalent)?
Thanks

Dyuman Joshi on 22 Feb 2024
Moved: Dyuman Joshi on 22 Feb 2024
Unfortunately, that is not possible.
The symbolic engine directly evaluates the function sec() to 1/cos() (and csc() to 1/sin()), see - https://in.mathworks.com/matlabcentral/answers/366337-matlab-symbolic-toolbox-deactivate-automatic-simplification#comment_3073193
Paul Dostert on 22 Feb 2024
Moved: Dyuman Joshi on 22 Feb 2024
Dyuman Joshi on 22 Feb 2024

Ayush Modi on 20 Feb 2024
Edited: the cyclist on 22 Feb 2024
Hi Paul,
MATLAB tends to automatically simplify trigonometric expressions to "sin", "cos", or "tan" where possible. There are no settings to avoid it. However as a work around, you can use strrep function to replace the output with the desired strings.
syms x;
expr = sec(x)^2
expr =
% Convert the expression to a string
exprStr = char(expr);
% Replace '1/cos' with 'sec' in the string
exprStr = strrep(exprStr, '1/cos', 'sec')
exprStr = 'sec(x)^2'
Note - This will not prevent the simplification of expression by MATLAB.
Paul Dostert on 20 Feb 2024
Thanks Ayush. I was hoping there was something along the lines of "trig = "six"" or something like that which would keep/simplify in terms of most efficient representations with all six trig functions. I ended up just hard-coding all of the integrals/derivatives using tan and sec. Thanks for your response thourgh.

John D'Errico on 22 Feb 2024
Edited: John D'Errico on 22 Feb 2024
The problem is, which form is simpler? Simple in your eyes need not always be simple in the "eyes" of your computer.
The point is, the simplification tool needs to make a decision, and that decision may not be your preference. Even if you told it to allow all 6 trig functions, there would be many fairly simple choices it could make.
syms theta
X = sec(theta)^2
X =
And that may seem simple to you, or not. It was the choice made by default, to use sin and cos where possible. But how about this one?
simplify(X,1000)
ans =
In my eyes, that seems pretty simple! But there are so many alternatives one could choose. A small subset is seen here:
simplify(X,'steps',100,'all',true)
ans =
Another option is to use rewrite:
rewrite(X,'sec')
Error using rewrite
Expected input to match one of these values:

'sincos', 'sin', 'cos', 'tan', 'cot', 'sinhcosh', 'sinh', 'cosh', 'tanh', 'coth', 'asin', 'acos', 'atan', 'acot', 'asinh', 'acosh', 'atanh', 'acoth', 'exp', 'log', 'sqrt', 'heaviside', 'piecewise', 'expandroot', 'expandsum', 'CGS', 'EMU', 'ESU', 'GU', 'SI', 'US'

The input, 'sec', did not match any of the valid values.
And rewrite sometimes works, but 'sec' was not an option.

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