Andrew's git / notes.git /
a119a4af35c22fc7724b9b2040a20b0634c3cabf
   1# Circular functions
   2
   3## Reciprocal functions
   4
   5### Cosecant
   6
   7$$\mathrm{cosec} \Theta = {1 \over \sin \Theta} \vert \sin \Theta \ne 0$$
   8
   9- **Domain** $= \mathbb{R} \ {n\pi : n \in \mathbb{Z}$
  10- **Range** $= \mathbb{R} \ (-1, 1)$
  11- **Turning points** at $\Theta = {{(2n + 1)\pi} \over 2} \vert n \in \mathbb{Z}$
  12- **Asymptotes** at $\Theta = n\pi \vert n \in \math{Z}$
  13
  14
  15### Secant
  16
  17$$\mathrm{sec} \Theta = {1 \over \cos \Theta} \vert \cos \Theta \ne =$$
  18
  19- **Domain** $= \mathbbb{R} \ \{{{(2n + 1) \pi} \over 2 } : n \in \mathbb{Z}\}$
  20- **Range** $= \mathbb{R} \ (-1, 1)$
  21- **Turning points** at $\Theta n \pi \vert n \in \mathbb{Z}$
  22- **Asymptotes** at $\Theta = {{(2n + 1) \pi} \over 2} \vert n \in \mathb{Z}$
  23
  24
  25### Cotangent
  26
  27$$\mathrm{cot} \Theta = {{\cos \Theta} \over {\sin \Theta}}$$