Here is a comparison between the terms you mentioned,while highlighting the meaning of 'determine': When 'identifying' anything, it is a voluntary action,where one does effort to sort out items ( or anything) from a larger groups and perceive them as belonging to the same class or being the same person or thing.It requires many times drawing a comparison between 2 things to 'discover' or 'find out' that they are one and the same such as fingerprints. This implies that the act of 'discovering' something is either accidentally or preceded by a certain effort. "After a lot of research, he discovered that the 2 substances were very different in nature." The act of 'determining' is when you conclude after observation or consideration.It is not really to 'discover the facts about something' ,but rather to 'shape ,influence or give direction to something. If all those actions were performed in succession, 'to find and discover' will precede the act of 'determining or identifying' whether items,numbers or any other specified entity. 'Determining' something relies on certain data or facts to be able to draw a conclusion as how a certain phenomena or thing should be quantitatively or qualitatively identified. In the process of 'determining' the size of a certain object for example, you need to 'identify' its height,length and breadth. In this case there is no place for chance or accident and here appears the 'calculation' as a notable factor for the act of 'determination'. You can discover by further search or the mere coincidence that the size of that specific object equals that of another one. In the case of a 'theory' as another example first there is a certain 'discovery' that follows observation and experimentation. A certain X ' finds' that certain variables act in a certain manner in certain conditions. Through experimentation his observations could rise to a theory. During experimenting he has to 'identify' the variables ,the way they act and the accompanied conditions, as in naming them and 'determining' their extent,scope ,size or any necessary quality. Here the act of 'determination' is a calculation and by no means a 'discovery'.

比如。。。有些句子 Discover （如果我们找到不寻常的东西） 1.后来发现他原来是间谍。 2.找两年，我最后找到金！ 3.我刚刚找到治疗癌症的方法！ Find （我们常常说"find"每个天。） 1.我找到我的帽子。 2.一个小时以后，我最后找到那个饭馆。

"Determine" in this case means to search for an answer and then to find it. It is not accidental like "discover" or "find," and it does not mean to recognize like "identify" does. Rather, it means to investigate something and reach a conclusion from what you learn. Examples: The police determined the identity of the man from his fingerprints. The engineers need to determine the cause of the system fault. The judge is trying to determine who is telling the truth.