Originally Posted by
HallsofIvy Now that's going to confuse a lot of people, Prove It!
More generally, tan and cotan, sin and cos, sec and csc "swap" complementary angles. That is, if $\displaystyle \theta$ and $\displaystyle \phi$ are the two non-right angles in a right triangle, then [tex]tan(\theta)= cot(\phi), $\displaystyle sin(\theta)= cos(\phi)$, [tex], and $\displaystyle sec(\theta)= csc(\phi)$. And, of course, those two angles add to $\displaystyle \frac{\pi}{2}$ (did I get it right, Prove It?).