From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Tue, 12 Mar 2019 01:19:36 +0000 (+1100)
Subject: [spec] circular functions (sec & cosec)
X-Git-Tag: yr12~213
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/c0501a1ff77f64d9d739dfe3281bc6265d7d2ad2

[spec] circular functions (sec & cosec)
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+# Circular functions
+
+## Reciprocal functions
+
+### Cosecant
+
+$$\mathrm{cosec} \Theta = {1 \over \sin \Theta} \vert \sin \Theta \ne 0$$
+
+- **Domain** $= \mathbb{R} \ {n\pi : n \in \mathbb{Z}$
+- **Range** $= \mathbb{R} \ (-1, 1)$
+- **Turning points** at $\Theta = {{(2n + 1)\pi} \over 2} \vert n \in \mathbb{Z}$
+- **Asymptotes** at $\Theta = n\pi \vert n \in \math{Z}$
+
+
+### Secant
+
+$$\mathrm{sec} \Theta = {1 \over \cos \Theta} \vert \cos \Theta \ne =$$
+
+- **Domain** $= \mathbbb{R} \ \{{{(2n + 1) \pi} \over 2 } : n \in \mathbb{Z}\}$
+- **Range** $= \mathbb{R} \ (-1, 1)$
+- **Turning points** at $\Theta n \pi \vert n \in \mathbb{Z}$
+- **Asymptotes** at $\Theta = {{(2n + 1) \pi} \over 2} \vert n \in \mathb{Z}$
+
+
+### Cotangent
+
+$$\mathrm{cot} \Theta = {{\cos \Theta} \over {\sin \Theta}}$$