From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Tue, 24 Jul 2018 00:31:03 +0000 (+1000)
Subject: add methods notes on solving trig equations
X-Git-Tag: yr11~82
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/1cb56c1fb7d4d43d4d519a4ad8c09378cbc1bbaf

add methods notes on solving trig equations
---

diff --git a/methods/circ-functions.md b/methods/circ-functions.md
index d232247..a4b06c0 100644
--- 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
 
 $$f(x)=a \sin(bx-c)+d$$
@@ -21,3 +23,16 @@ Domain is $\mathbb{R}$
 Range is $[-b+c, b+c]$;
 
 Graph of $\cos(x)$ starts at $(0,1)$. Graph of $\sin(x)$ starts at $(0,0)$.
+
+**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 $n$
+
+$\sin2\theta={\sqrt{3}\over2}, \quad \theta \in[0, 2\pi] \quad(\therefore 2\theta \in [0,4\pi])$
+$2\theta=\sin^{-1}{\sqrt{3} \over 2}$
+$2\theta={\pi\over 3}, {2\pi \over 3}, {7\pi \over 3}, {8\pi \over 3}$
+$\therefore \theta = {\pi \over 6}, {\pi \over 3}, {7 \pi \over 6}, {4\pi \over 3}$