simplify symbolic trigonometric expression

Question

Mohd Aaquib Khan 2022-10-24

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1833948-simplify-symbolic-trigonometric-expression

编辑： Ishu 2023-10-3

I get a big and jumbled up symbolic output and there are many cos and sines but they dont simplify although I can spot many places where they can combine. Below is a small example where just b is simplified as intended but (b+1) is not.

I know I can add steps but the one below is just an example, I have a big expression (a PART of it is shown below) and I tried even 10k steps but no luck, not to mention that it takes forever with steps added.

If anyone has any ideas then I would be thankful.

actual expression - 50*cos(a) - 50*sin(a) + 425*cos(a)*sin(b) - 100*sin(a)*sin(d)*sin(e) + 100*sin(b + c)*cos(a)*cos(e) + 425*cos(a)*cos(b)*sin(c) + 425*cos(a)*cos(c)*sin(b) + 100*cos(a)*cos(b)*cos(c)*cos(d)*sin(e) - 100*cos(a)*cos(d)*sin(b)*sin(c)*sin(e)

I can spot 2 terms that can combine but it doesnt happen for some reason.

syms x y z k m

b = cos(y)*cos(z)*cos(x) - sin(y)*sin(z)*cos(x)

b =

simplify(b)

ans =

simplify(b+1)

ans =

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Answer 1

Ishu 2023-8-31

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在 MATLAB Online 中打开

Hi Mohd Aaquib,

You can resolve this by breaking down the equation means you can combine the similar expressions and then simplify those parts separately and then at last you can combine then and then simplify the whole expression.

Like in your expression you can breakdown as:

syms a b c d e

eq1 = 50*cos(a) - 50*sin(a);

eq1 = simplify(eq1)

eq1 =

eq2 = simplify(425*cos(a)*sin(b))

eq2 =

eq3 = simplify(- 100*sin(a)*sin(d)*sin(e) + 100*sin(b + c)*cos(a)*cos(e))

eq3 =

eq4 = simplify(425*cos(a)*cos(b)*sin(c) + 425*cos(a)*cos(c)*sin(b))

eq4 =

eq5 = simplify(100*cos(a)*cos(b)*cos(c)*cos(d)*sin(e) - 100*cos(a)*cos(d)*sin(b)*sin(c)*sin(e))

eq5 =

Now you can combine these equations('eq1' to 'eq5') and then simplify the whole expression. Or you can also look for more similar expressions like in 'eq2' and 'eq4', simplify these first and then simplify the whole result.

For more information you can refer to this documentation:

https://www.mathworks.com/help/symbolic/simplify-symbolic-expressions.html?searchHighlight=simplify%20trigonometric&s_tid=srchtitle_support_results_6_simplify%2520trigonometric

Hope it helps!