The choice was based on a misreading of the Arabic written form j-y-b (جيب), which itself originated as a transliteration from Sanskrit jīvā, which along with its synonym jyā (the standard Sanskrit term for the sine) translates to 'bowstring', being in turn adopted from Ancient Greek χορδή 'string'.
The word sine derives from Latin sinus, meaning 'bend bay', and more specifically 'the hanging fold of the upper part of a toga', 'the bosom of a garment', which was chosen as the translation of what was interpreted as the Arabic word jaib, meaning 'pocket' or 'fold' in the twelfth-century translations of works by Al-Battani and al-Khwārizmī into Medieval Latin. From Wikipedia - Trigonometric Functions - Etymology
