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    Why does the Unit Circle work?

    In my Trig class, we learned about the unit circle and its relationship to the various trig functions (sin, cos, etc.). I am curious to know why the unit circle works the way it does, and the how it was "derived" so to speak. More specifically, why does radius of the circle have to be 1 for...
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    Dividing by Zero=undefined or complex infinite?

    Thank you all for your explanations. Hopefully I'll gain a better understanding of this advance concept in the future.
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    Dividing by Zero=undefined or complex infinite?

    Would it be possible for you to explain this in laymen's terms, seeing as I am only in precalculus. Thank you
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    Dividing by Zero=undefined or complex infinite?

    A few days ago, I had a problem that looked like this: evaluate cot(pi) I know that on the unit circle, cot(pi) ends up as -1/0. In my precalc class, we say that this is undefined because you can't divide by zero. I decided to plug the problem into wolfram and it tells me that there is...
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    Defining negative logarithms

    I recently had a test (precalc) where we had to solve log(x)-log(x+4)=2 for x. The answer comes out negative. I understand that in precalc we are defining the logarithms for just positive numbers, but- Is it ever justified to define a logarithm for all numbers, both negative and...