From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Wed, 13 Mar 2019 07:10:07 +0000 (+1100)
Subject: [spec] graphics for reciprocal circular functions
X-Git-Tag: yr12~210
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/394d40a01334eb57a2b01c63167d4299b7107dc1

[spec] graphics for reciprocal circular functions
---

diff --git a/spec/circ.md b/spec/circ.md
index 8f3fcec..9d7dfbf 100644
--- a/spec/circ.md
+++ b/spec/circ.md
@@ -1,9 +1,16 @@
 # Circular functions
 
+Period of $a\sin(bx)$ is ${2\pi} \over b$
+
+Period of $a\tan(nx)$ is $\pi \over n$  
+Asymptotes at $x={2k+1)\pi \over 2n} \> \vert \> k \in \mathbb{Z}$
+
 ## Reciprocal functions
 
 ### Cosecant
 
+![](graphics/csc.png)
+
 $$\operatorname{cosec} \theta = {1 \over \sin \theta} \> \vert \> \sin \theta \ne 0$$
 
 - **Domain** $= \mathbb{R} \setminus {n\pi : n \in \mathbb{Z}}$
@@ -14,6 +21,8 @@ $$\operatorname{cosec} \theta = {1 \over \sin \theta} \> \vert \> \sin \theta \n
 
 ### Secant
 
+!()[graphics/sec.png]
+
 $$\operatorname{sec} \theta = {1 \over \cos \theta} \> \vert \> \cos \theta \ne 0$$
 
 - **Domain** $= \mathbb{R} \setminus \{{{(2n + 1) \pi} \over 2 } : n \in \mathbb{Z}\}$
@@ -24,6 +33,8 @@ $$\operatorname{sec} \theta = {1 \over \cos \theta} \> \vert \> \cos \theta \ne
 
 ### Cotangent
 
+!()[graphics/cot.png]
+
 $$\operatorname{cot} \theta = {{\cos \theta} \over {\sin \theta}} \> \vert \> \sin \theta \ne 0$$
 
 - **Domain** $= \mathbb{R} \setminus \{n \pi: n \in \mathbb{Z}\}$
diff --git a/spec/graphics/cot.png b/spec/graphics/cot.png
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diff --git a/spec/graphics/csc.png b/spec/graphics/csc.png
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diff --git a/spec/graphics/sec.png b/spec/graphics/sec.png
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