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{#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- {#id .class width=40%} The angle at the centre of a circle is twice the angle at the circumference subtended by the arc 46- {#id .class width=40%} the angle in a semicircle is a right angle 47- {#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$$|x|=\sqrt{x^2}$$