From: Andrew Lorimer 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?hp=587467507e324411130472d15053ee564aa1a3ea start prelim notes --- diff --git a/spec/graphics/circle-centre-angles.png b/spec/graphics/circle-centre-angles.png new file mode 100644 index 0000000..8d0bb30 Binary files /dev/null and b/spec/graphics/circle-centre-angles.png differ diff --git a/spec/graphics/segment-angles.png b/spec/graphics/segment-angles.png new file mode 100644 index 0000000..63851d7 Binary files /dev/null and b/spec/graphics/segment-angles.png differ diff --git a/spec/graphics/semicircle-right-angle.png b/spec/graphics/semicircle-right-angle.png new file mode 100644 index 0000000..2e11cf3 Binary files /dev/null and b/spec/graphics/semicircle-right-angle.png differ diff --git a/spec/graphics/transversal.png b/spec/graphics/transversal.png new file mode 100644 index 0000000..35195b8 Binary files /dev/null and b/spec/graphics/transversal.png differ diff --git a/spec/prelim.md b/spec/prelim.md new file mode 100644 index 0000000..d53e5ef --- /dev/null +++ b/spec/prelim.md @@ -0,0 +1,44 @@ +# 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 +- ![]()