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I've seen a lot of diagrams that are kind of like this over the years, but most of them are static and incomplete and a little bit ugly.  Here's an interactive pretty one!

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Trigonometric function visualization

Here's an interactive diagram of how the six trig functions are defined. Click and drag to change the angle. Now you can see where the names "tangent" and "secant" come from, as well as what the "co" prefix is doing in there.

Comments

Jake Eakle

I can't figure out what the "alternate views" mentioned in the text are — I'm only seeing one thing labeled with each function name.