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## What is tangent?

Trig functions have a lot of acronyms. Is this good or bad, well I don’t know. What I do know is this: tangent is much more than just sine over cosine or opposite over adjacent. However, the text books I teach from usually focus on that. So, I thought I would make an investigation that allows students to see that tangent can also be seen as length of the tangent line to the unit circle at $(0,1)$ Wikipedia gives some good pictures. Click here to see the article.

Note the location of tangent and secant

I also like in the article when it writes about “Slope Definitions”.

“Tangent combines the rise and run” meaning that Tangent takes the angle of the line segment and tells its slope; or alternatively, tells the vertical rise when the line segment’s horizontal run is 1.

So, next time you talk about the trig functions be sure to expand on the idea of tangent. Here is a Desmos graph I made that you can use. Click on the image to see the graph.