The Indian word for what we call sine was 'jyā'. The Surya-siddhanta mentions 'jyā' many many times. As does the Aryabhatiya. In contrast they mention the synonym 'jivā' only once or twice. So why was 'jiva' transliterated into Arabic rather than 'jyā'? It makes no sense; 'Jyā' is written all over these texts and 'jivā' is not. Did later Indian mathematicians perhaps use 'jivā' more often? Was it one particular Arabic translator who translated a particular Indian text which happened to use 'jivā' rather than 'jyā'?
The unabridged Oxford English Dictionary, which is quite authentic does not trace sine to any Sanskrit words
Etymology: < Latin sinus a bend, bay, etc.; also, the hanging fold of the upper part of a toga, the bosom of a garment, and hence used to render the synonymous Arabic jaib , applied in geometry as in sense 2. Compare French sinus, Spanish seno, Italian seno.
However, a book by A. Bello, Origins of mathematical words: a comprehensive dictionary of Latin, Greek, and Arabic roots states the following
Regardless the sad thing nobody has ever produced even images of original documents of Sanskrit, or even the authors. So take everything as a grain of salt especially the stories on Wikipedia. I am curious to see any original source and the name of the Sanskrit speaking author who first used those words.