ed06b09db8ad416577a72c0d21ee35889b9363de
   1# Preliminary topics
   2
   3## Circular functions
   4
   5$\sin \theta$ - $y$-coord on unit circle  
   6$\cos \theta$ - $x$-coord on unit circle  
   7$\tan \theta = {\sin \theta \over \cos \theta}$
   8
   9$1^\text{c}= {180^\circ \over \pi}  \quad \text{or} \quad 1^\circ = {\pi^\text{c} \over 180}$
  10
  11period = $2 \pi \over n$
  12
  13## Sine and cosine rules
  14
  15### Sine rule
  16
  17$${a \over \sin A}={b \over \sin B}={c \over \sin c}$$
  18
  19### Cosine rule
  20
  21$$a^2=b^2 - 2bc \cos A$$
  22
  23## Geometry
  24
  25### Area of a triangle
  26
  27$A={1 \over 2} a b \sin C$
  28
  29### Parallel lines
  30
  31If parallel lines are crossed by transversal:
  32
  33- alternate angles are equal
  34- corresponding angles are equal
  35- co-interior angles are supplementary
  36
  37![](graphics/transversal.png){#id .class width=40%}
  38
  39### Angles in a polygon
  40
  41Sum of interior angles of $n$-sided polygon is $(n-2) \times 180^\circ$
  42
  43### Circle geometry
  44
  45- ![](graphics/circle-centre-angles.png){#id .class width=40%} The angle at the centre of a circle is twice the angle at the circumference subtended by the arc
  46- ![](graphics/semicircle-right-angle.png){#id .class width=40%} the angle in a semicircle is a right angle
  47- ![](graphics/segment-angles.png){#id .class width=40%} angles in the same segment of a circle are equal
  48- ![]()
  49
  50
  51## Ellipses and hyperbolas
  52
  53#### Ellipses
  54
  55$${(x-h)^2 \over a^2}+{(y-k)^2 \over b^2} = 1$$
  56
  57#### Hyperbolas
  58
  59$${(x-h)^2 \over a^2} - {(y-k)^2 \over b^2} = 1$$
  60
  61- centre at $(h,k)$
  62- asymptotes at $y-k=\pm{b \over a}(x-h)$
  63
  64${(x-h)^2 \over a^2} - {(y-k)^2 \over b^2} = 1$ and ${(y-k)^2 \over b^2} - {(x-h)^2 \over a^2} = 1$ are **conjugate hyperbolas**
  65
  66## Modulus function
  67
  68$$|x|=\sqrt{x^2}$$