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

Question

Paul Dostert 2024-1-31

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编辑： John D'Errico 2024-2-22

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

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Answer 1

Dyuman Joshi 2024-2-22

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移动：Dyuman Joshi 2024-2-22

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

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Paul Dostert 2024-2-22

移动：Dyuman Joshi 2024-2-22

Dyuman, You mind adding that as an answer instead of a comment so I can accept and close the thread. Thanks for your help!

Dyuman Joshi 2024-2-22

@Paul Dostert, done.

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Answer 2

Ayush Modi 2024-2-20

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编辑：the cyclist 2024-2-22

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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.

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Paul Dostert 2024-2-20

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.

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Answer 3

John D'Errico 2024-2-22

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编辑：John D'Errico 2024-2-22

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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.