Andrew's git
/
notes.git
/ diff
summary
|
log
|
commit
| diff |
tree
commit
grep
author
committer
pickaxe
?
re
add more on polar graphing
author
Andrew Lorimer
<andrew@lorimer.id.au>
Thu, 2 Aug 2018 06:51:36 +0000
(16:51 +1000)
committer
Andrew Lorimer
<andrew@lorimer.id.au>
Thu, 2 Aug 2018 06:51:36 +0000
(16:51 +1000)
spec/graphing.md
patch
|
blob
|
history
raw
|
patch
|
inline
| side by side (parent:
f50ad8f
)
diff --git
a/spec/graphing.md
b/spec/graphing.md
index 39b748d0ffe73a8e18c3d41eb18347a0be3737bc..6829ab158300869b17fdc31fddcf9b72a0fd76f2 100644
(file)
--- 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):
$${(x-h)^2 \over a^2} - {(y-k)^2 \over b^2} = 1$$
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 $y$
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: $r={n \over \cos \theta}$
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 $r$
### 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
$r^2=6r\cos\theta$
$x^2+y^2=6x$
complete the square
-
-## Other graphs
-
-### Cardioids
-
-$$
-
-### Roses