<prompt> Hlalosa ka mantsoe a hao hore na cosine ke eng.nan  <response>: Instruction in English: Describe in your own words what is cosine similarity. . Response in English: Cosine similarity is a measure used to calculate the similarity between two non-zero vectors. It calculates the cosine of the angle between these two vectors projected in a multi-dimensional space. Represented mathematically, the cosine similarity is the dot product of two vectors divided by the product of the vectors magnitude. In other words, it measures how similar the vectors direction is, ignoring their magnitudes. Cosine similarity is useful in various applications, such as text analysis, recommendation systems, and search engines, where the magnitude of vectors is not as important as their orientation. The similarity score lies within the range of -1 to 1 where 1 indicates that the two vectors are identical, 0 indicates that two vectors are orthogonal, and -1 means that the vectors are diametrically opposed. . Response in Sesotho: Ho tšoana ha cosine ke tekanyo e sebelisoang ho bala ho tšoana ho teng lipakeng tsa li-vector tse peli tseo e seng zero. E lekanya cosine ea angle pakeng tsa li-vector tsena tse peli tse hlahisoang sebakeng se nang le mahlakore a mangata. E emetsoe ka lipalo, ho tšoana ha cosine ke sehlahisoa sa matheba a li-vector tse peli tse arotsoeng ka sehlahisoa sa boholo ba vector. Ka mantsoe a mang, e lekanya hore na tataiso ea li-vector e tšoana hakae, e hlokomoloha boholo ba tsona. Ho tšoana ha Cosine ho molemo litsebetsong tse fapaneng, joalo ka tlhahlobo ea mongolo, litsamaiso tsa likhothaletso, le lienjine tsa ho batla, moo boholo ba li-vector bo seng bohlokoa joalo ka maikutlo a tsona. Palo ea ho tšoana e ka hara moeli oa -1 ho isa ho 1 moo 1 e bontšang hore li-vector tse peli li tšoana, 0 e bontša hore li-vector tse peli li na le orthogonal, me -1 e bolela hore li-vector li hanyetsana ka bophara. 