Geodesic
Expansion of the element~$\sin a$ in exponentials for Hermitian~$a$
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 28, Tome 270 (2000), pp. 253-257

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Let $A$ be a complex Banach algebra with identity and $a\in A$ a Hermitian element. An interpolation formula is proved expressing $\sin a$ in terms of exponentials and implying, in particular, the identity $\|\sin a\|=|\sin a|$. 
@article{ZNSL_2000_270_a10,
     author = {H. S. Mustafaev and M. T. Karaev},
     title = {Expansion of the element~$\sin a$ in exponentials for {Hermitian~}$a$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {253--257},
     publisher = {mathdoc},
     volume = {270},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_270_a10/}
}
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H. S. Mustafaev; M. T. Karaev. Expansion of the element~$\sin a$ in exponentials for Hermitian~$a$. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 28, Tome 270 (2000), pp. 253-257. http://geodesic.mathdoc.fr/item/ZNSL_2000_270_a10/