I have seen a Taylor series derivation of the trig functions with an infinite series, but I wanted to see if it is possible to derive these trig functions using geometry instead of derivatives. How can we prove that sine, cosine, and tangent are always ratios of triangle lengths?
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In this answer, I describe a connection between sine and cosine as power series and as legs of a unit right triangle. This older answer discusses tangent and secant. – Blue Nov 07 '19 at 22:20
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The usual definitions of trig functions are in terms of ratios of side lengths of right triangles. What definitions are you proposing to use instead? – herb steinberg Nov 07 '19 at 22:20
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1Thanks Blue, I couldn't find those posts when I was searching, but those were just what I was looking for. – IPrayToMath Nov 07 '19 at 22:59