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February 13th, 2016, 05:21 PM   #1
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Conceptual Understanding of Trigonometry

I'm currently taking Calculus I in highschool. As I started to read a bit about the derivatives of trigonometric functions, I made the realization that I have no idea what the significance of sec, csc, and cot, or even tan for that matter, is. I understand that they are reciprocal functions, and that tan is the ratio of the sin to the cos, but why do we even have these? Why are they their own dedicated functions?

Could anyone recommend a book/resource that will help me a develop a conceptual and thorough understanding of all things trigonometry?

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February 13th, 2016, 06:18 PM   #2
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I don't think you need a book... What you do need is to play with the graphs of these functions a bit. Then you'll realise why, for example, differentiating sin x gets you cos x.
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February 14th, 2016, 06:27 PM   #3
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Convenience, if nothing else. All trigonometric functions can be written in terms of sine and/or cosine.
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February 15th, 2016, 10:53 AM   #4
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A right triangle has three sides, a, b, and c, say. There are 3 ways to take them 2 at a time: ab, ac, and bc. Including different orders, there are 6: ab, ac, ba, ca, ab, and ba. "sine", "cosine", "secant", "cosecant", "tangent", and "cotangent". That is, those functions are all the different ways of comparing pairs of sides of a right triangle.
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February 27th, 2016, 09:05 PM   #5
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If you're still looking for a book, I highly recommend the good old "Pre-Calculus for Dummies". They even have a Trigonometry for dummies, but I never got that one. The Pre-Calculus for Dummies book has a good amount of Trig in it, and proved to be very helpful to me in the past and still today!
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