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Why in trigonometric function, our teacher said that we can use the formula: symbol to see quadrant when simplifying or calculating. But why not sometimes?
The complete formula is "odd couple, the sign looks at the quadrant, one is positive and two is sine, three is tangent and four is cosine".

You must fully understand the formula before using it, otherwise some problems will appear. This formula has existed for many years and there will be no problem. You must have overlooked some detail, so check it again.

Hope to adopt, if you don't understand, welcome to ask questions.