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It turns out that Sage's various interpreters do have ways to get matrix trig functions :

giac has matrix trig functions :

sage: matrix(giac.sin(A)._sage_()) [ sin(2) -sin(2) + sin(1) -3sin(2) + 3sin(1)] [-3sin(2) + 3sin(1) 3sin(2) - 2sin(1) 9sin(2) - 9sin(1)] [ sin(2) - sin(1) -sin(2) + sin(1) -3sin(2) + 4sin(1)]
sympy has not matrix trig functions. But it has matrix exponential (and logarithm), which can be used to find matrix trigonoimetric functions, as noted by @Max Alekseyev :

sage: matrix([[u for u in v] for v in ((IA)._sympy_().exp()-(-IA)._sympy_().ex ....: p())._sage_()/2/I]).apply_map(lambda u:u.demoivre(force=True)) [ sin(2) -sin(2) + sin(1) -3sin(2) + 3sin(1)] [-3sin(2) + 3sin(1) 3sin(2) - 2sin(1) 9sin(2) - 9sin(1)] [ sin(2) - sin(1) -sin(2) + sin(1) -3sin(2) + 4sin(1)]
You can cheat and use Mathematica, or the (gratis but not free) Wolfram engine :

age: matrix(sin._mathematica_().MatrixFunction(A).sage()) [ sin(2) -sin(2) + sin(1) -3sin(2) + 3sin(1)] [-3sin(2) + 3sin(1) 3sin(2) - 2sin(1) 9sin(2) - 9sin(1)] [ sin(2) - sin(1) -sin(2) + sin(1) -3sin(2) + 4sin(1)]

One notes that conversions of matrices to/from interpreters may be problematic which implies some workarounds in the previous examples...

HTH,

It turns out that Sage's various interpreters do have ways to get matrix trig functions :

giac has matrix trig functions :

sage: matrix(giac.sin(A)._sage_()) [ sin(2) -sin(2) + sin(1) -3sin(2) + 3sin(1)] [-3sin(2) + 3sin(1) 3sin(2) - 2sin(1) 9sin(2) - 9sin(1)] [ sin(2) - sin(1) -sin(2) + sin(1) -3sin(2) + 4sin(1)]
sympy has not matrix trig functions. But it has matrix exponential (and logarithm), which can be used to find matrix trigonoimetric functions, as noted by @Max Alekseyev :

sage: matrix([[u for u in v] for v in ((IA)._sympy_().exp()-(-IA)._sympy_().ex ....: p())._sage_()/2/I]).apply_map(lambda u:u.demoivre(force=True)) [ sin(2) -sin(2) + sin(1) -3sin(2) + 3sin(1)] [-3sin(2) + 3sin(1) 3sin(2) - 2sin(1) 9sin(2) - 9sin(1)] [ sin(2) - sin(1) -sin(2) + sin(1) -3sin(2) + 4sin(1)]
You can cheat and use Mathematica, or the (gratis but not free) Wolfram engine :

~~age:~~ sage: matrix(sin._mathematica_().MatrixFunction(A).sage()) [ sin(2) -sin(2) + sin(1) -3sin(2) + 3sin(1)] [-3sin(2) + 3sin(1) 3sin(2) - 2sin(1) 9sin(2) - 9sin(1)] [ sin(2) - sin(1) -sin(2) + sin(1) -3sin(2) + 4sin(1)]

One notes that conversions of matrices to/from interpreters may be problematic which implies some workarounds in the previous examples...

HTH,

It turns out that Sage's various interpreters do have ways to get matrix trig functions :

giac has matrix trig functions :

~~sage: matrix(giac.sin(A)._sage_()) [ sin(2) -sin(2) + sin(1) -3sin(2) + 3sin(1)] [-3sin(2) + 3sin(1) 3sin(2) - 2sin(1) 9sin(2) - 9sin(1)] [ sin(2) - sin(1) -sin(2) + sin(1) -3sin(2) + 4sin(1)]~~

-3*sin(2) + 3*sin(1)] [-3*sin(2) + 3*sin(1) 3*sin(2) - 2*sin(1) 9*sin(2) - 9*sin(1)] [ sin(2) - sin(1) -sin(2) + sin(1) -3*sin(2) + 4*sin(1)]
sympy has not matrix trig functions. But it has matrix exponential (and logarithm), which can be used to find matrix trigonoimetric functions, as noted by @Max Alekseyev :

sage: matrix([[u for u in v] for v in ((IA)._sympy_().exp()-(-IA)._sympy_().ex ((I*A)._sympy_().exp()-(-I*A)._sympy_().ex ....: p())._sage_()/2/I]).apply_map(lambda u:u.demoivre(force=True)) [ sin(2) -sin(2) + sin(1) -3sin(2) + 3sin(1)] [-3sin(2) + 3sin(1) 3sin(2) - 2sin(1) 9sin(2) - 9sin(1)] [ sin(2) - sin(1) -sin(2) + sin(1) -3sin(2) + 4sin(1)]

-3*sin(2) + 3*sin(1)] [-3*sin(2) + 3*sin(1) 3*sin(2) - 2*sin(1) 9*sin(2) - 9*sin(1)] [ sin(2) - sin(1) -sin(2) + sin(1) -3*sin(2) + 4*sin(1)]
You can cheat and use Mathematica, or the (gratis but not free) Wolfram engine :

sage: matrix(sin._mathematica_().MatrixFunction(A).sage()) [ sin(2) -sin(2) + sin(1) -3sin(2) + 3sin(1)] [-3sin(2) + 3sin(1) 3sin(2) - 2sin(1) 9sin(2) - 9sin(1)] [ sin(2) - sin(1) -sin(2) + sin(1) -3sin(2) + 4sin(1)]

-3*sin(2) + 3*sin(1)]
[-3*sin(2) + 3*sin(1)  3*sin(2) - 2*sin(1)  9*sin(2) - 9*sin(1)]
[     sin(2) - sin(1)     -sin(2) + sin(1) -3*sin(2) + 4*sin(1)]

One notes that conversions of matrices to/from interpreters may be problematic which implies some workarounds in the previous examples...

HTH,

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