Merge branch 'master' of ssh://charles/tank/andrew/school/notes

locuses (spec), equilibrium for circ fn's (methods - merge w/ruslan), solvent eq's (chem)

diff --git a/chem/water.md b/chem/water.md
index 9635ed669e3f57625fe7f77ffd97ad536c79ce07..3b1ccf9d5ef6da938760d4c038ff9c8ede0ea374 100644 (file)
--- a/chem/water.md
+++ b/chem/water.md
@@ -73,3 +73,4 @@
 ## Concentration
 - amount of solute per volume of solvent - e.g. g / L
 - relative terms - "concentrated" or "dilute"
+- mg / L = ppm = $\mu$g / g

diff --git a/methods/circ-functions.md b/methods/circ-functions.md
index a48b106a03b2820f6413371572302a9c9bc26859..3bbe1c238fc68a6543734b9d89b464b7438565e5 100644 (file)
--- a/methods/circ-functions.md
+++ b/methods/circ-functions.md
@@ -6,6 +6,8 @@ $$1 \thinspace \operatorname{rad}={{180 \operatorname{deg}}\over \pi}$$
 
 ## Exact values
 
+
+
 ## $\sin$ and $\cos$ graphs
 
 $$f(x)=a \sin(bx-c)+d$$
@@ -22,6 +24,20 @@ Range is $[-b+c, b+c]$;
 
 Graph of $\cos(x)$ starts at $(0,1)$. Graph of $\sin(x)$ starts at $(0,0)$.
 
+<<<<<<< HEAD
+**Mean / equilibrium:** line that the graph oscillates around ($y=d$)
+
+## Solving trig equations
+
+1. Solve domain for $n\theta$
+2. Find solutions for $n\theta$
+3. Divide solutions by $n$
+
+$\sin2\theta={\sqrt{3}\over2}, \quad \theta \in[0, 2\pi] \quad(\therefore 2\theta \in [0,4\pi])$
+$2\theta=\sin^{-1}{\sqrt{3} \over 2}$
+$2\theta={\pi\over 3}, {2\pi \over 3}, {7\pi \over 3}, {8\pi \over 3}$
+$\therefore \theta = {\pi \over 6}, {\pi \over 3}, {7 \pi \over 6}, {4\pi \over 3}$
+=======
 ### Amplitude
 
 Amplitude of $a$ means graph oscillates between $+a$ and $-a$ in $y$-axis
@@ -71,3 +87,4 @@ period $T$ is $\pi \over n$
 range is $R$
 roots at $x={k\pi \over n}$
 asymptotes at $x={{(2k+1)\pi}\over 2},\quad k \in \mathbb{Z}$
+>>>>>>> 924c0548b3e7564d4015e879c56a46a5606807fe

diff --git a/spec/graphing.md b/spec/graphing.md
index 3e889a062083bb7894eedf5007046f2b9c32fb3d..6cd013e79389e1a7f92b4a8566f0d4c3c2032e60 100644 (file)
--- a/spec/graphing.md
+++ b/spec/graphing.md
@@ -91,7 +91,8 @@ $$|(F_2P - F_1P  )| = k$$
 Cartesian equation for hyperbolas ($a$ and $b$ are dilation factors):
 $${(x-h)^2 \over a^2} - {(y-k)^2 \over b^2} = 1$$
 
-Asymptotes at $y-k=\pm {b \over a}(x-h$)
+Asymptotes at $y=\pm {b \over a}(x-h)+k$
+To make hyperbola up/down rather than left/right, swap $x$ and $y$
 
 ## Parametric equations