I somehow missed Trig in high school and college. Feeling left out, I set out to teach it to myself. I have the basic understanding of trig so far. But I have two questions that urk myself because I am unable to find the answer. I am using khan academy as my main resource. If you have any other great (free) resources, I'd be sincerely interested. Also, if you have any resources that gives out quote unquote 'homework', I'd be interested in that as well.
1. I understand that sin, cos, tan, and etc. is a ratio of side lengths to angles. But who discovered this where? And why? And how? How do you prove it works? (I hate to just assume that it works.) [edit] I hate to assume that soh cah toa works just because some guy on the internet says so. Can you prove to me that sine is equal to opposite over hypotenuse? Same with cosine and tangent? [/edit]
2. I understand the Unit Circle and its creation except for one part. Except for the 0* / 360*, 90*, and 180*, where do the coordinate values come from? Every resource I find has 'tricks' to remember it. No explanation on how to prove the value stated is the true coordinate point.
I suggest you to get this book which is really good and attractive for beginners and also intermediate students:
College Algebra and Trigonometry, 3rd Edition
And this online source is enough for basic trigonometry:
FlashCard instructions