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Sine & Sina are shortened versions of various longer names, e.g. Olsine, Hansine, Jensine, Tomasine, Nilsine, Larsine etc (variant forms ending in '-na' also possible). So there isn't really any independent meaning to stand-alone forms like Sine and Sina.

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Spelling 'Sena' most likely stems from an English language environment.

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Only 9 persons in the 1900 census had names ending in '-sena'. (Two of them just 'Sena'.
42 had names ending in '-sene'.
1890 had names ending in '-sina'.
9687 had names ending in '-sine'.