From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Thu, 2 Aug 2018 06:51:36 +0000 (+1000)
Subject: add more on polar graphing
X-Git-Tag: yr11~78
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/8a67af4d02d05e3b50fb3159cb24669d995484d4?ds=sidebyside

add more on polar graphing
---

diff --git a/spec/graphing.md b/spec/graphing.md
index 39b748d..6829ab1 100644
--- a/spec/graphing.md
+++ b/spec/graphing.md
@@ -91,6 +91,9 @@ $$|(F_2P - F_1P  )| = k$$
 Cartesian equation for hyperbolas ($a$ and $b$ are dilation factors):
 $${(x-h)^2 \over a^2} - {(y-k)^2 \over b^2} = 1$$
 
+Distance between vertices is $2a$
+Vertices given by $(h \pm a, k)$
+
 Asymptotes at $y=\pm {b \over a}(x-h)+k$
 To make hyperbola up/down rather than left/right, swap $x$ and $y$
 
@@ -121,6 +124,19 @@ $$r=a$$
 Horizontal: $r={n \over \sin \theta}$
 Vertical: $r={n \over \cos \theta}$
 
+### Cardioids
+
+$$r=a(n+ \cos\theta)$$
+
+### Roses
+
+$$r=\cos(k\theta)$$
+
+where
+If $k$ is odd, half of the petals will overlap (hence there are $n$ petals)
+If $k$ is even, petals will not overlap (hence $2n$ petals)
+
+
 ### Solving polar graphs
 
 solve in terms of $r$
@@ -138,11 +154,3 @@ e.g. $r=6\cos \theta\quad$ *(multiple by $r$)*
 $r^2=6r\cos\theta$
 $x^2+y^2=6x$
 complete the square
-
-## Other graphs
-
-### Cardioids
-
-$$
-
-### Roses