From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Thu, 29 Nov 2018 00:04:23 +0000 (+1100)
Subject: start prelim notes
X-Git-Tag: yr12~292
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/546a68fcd502da1c56dffee420767f4000cc499b

start prelim notes
---

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+# Preliminary topics
+
+## Circular functions
+
+$\sin \theta$ - $y$-coord on unit circle  
+$\cos \theta$ - $x$-coord on unit circle  
+$\tan \theta = {\sin \theta \over \cos \theta}$
+
+$1^\text{c}= {180^\circ \over \pi}  \quad \text{or} \quad 1^\circ = {\pi^\text{c} \over 180}$
+
+period = $2 \pi \over n$
+
+## Sine and cosine rules
+
+### Sine rule
+
+$${a \over \sin A}={b \over \sin B}={c \over \sin c}$$
+
+### Cosine rule
+
+$$a^2=b^2 - 2bc \cos A$$
+
+## Geometry
+
+### Parallel lines
+
+If parallel lines are crossed by transversal:
+
+- alternate angles are equal
+- corresponding angles are equal
+- co-interior angles are supplementary
+
+![](graphics/transversal.png){#id .class width=40%}
+
+### Angles in a polygon
+
+Sum of interior angles of $n$-sided polygon is $(n-2) \times 180^\circ$
+
+### Circle geometry
+
+- ![](graphics/circle-centre-angles.png) The angle at the centre of a circle is twice the angle at the circumference subtended by the arc
+- ![](graphics/semicircle-right-angle.png) the angle in a semicircle is a right angle
+- ![](graphics/segment-angles.png) angles in the same segment of a circle are equal
+- ![]()