Tangent

Hello, everyone, I'm back from my year-long absence. I promised that I'd write about the tangent (tan) that went with sine and cosine in trigonometry, so here goes. First, we take the same triangle we used for the sine and cosine.



Let's use the same axes, too.



On the first triangle, A, B, and C still represent the sizes of the angles in degrees. The little a, b, and c represent the lengths of each side. Here's how they combine to form tangential measurements:

tanA=a/c
tanC=c/a

Remember the "Toa" part of "SohCahToa"? It stands for tangent equals opposite over adjacent. On the axis drawing, x is adjacent and y is opposite, so

tanθ=y/x