## Circular functions
+{#id .class height=150px}
+{#id .class height=150px}
+
$\sin \theta$ - $y$-coord on unit circle
$\cos \theta$ - $x$-coord on unit circle
$\tan \theta = {\sin \theta \over \cos \theta}$
## Geometry
+### Area of a triangle
+
+$A={1 \over 2} a b \sin C$
+
### Parallel lines
If parallel lines are crossed by transversal:
### Circle geometry
--  The angle at the centre of a circle is twice the angle at the circumference subtended by the arc
--  the angle in a semicircle is a right angle
--  angles in the same segment of a circle are equal
+- {#id .class width=40%} The angle at the centre of a circle is twice the angle at the circumference subtended by the arc
+- {#id .class width=40%} the angle in a semicircle is a right angle
+- {#id .class width=40%} angles in the same segment of a circle are equal
- ![]()
+
+## Circles, ellipses and hyperbolas
+
+Standard form is $Ax^2+By^2+Cx+Dy=0$
+
+- if $A+B$ then circle
+- if $A>0$ and $B>0$ and $A\ne B$ then ellipse
+- if $A<0<B$ or $B<0<A$ then hyperbola
+
+### Circles
+
+$$(x-h)^2 + (y-k)^2 = r^2$$
+
+- centre $(h,k)$
+- radius $r$
+
+### Ellipses
+
+$${(x-h)^2 \over a^2}+{(y-k)^2 \over b^2} = 1$$
+
+- centre $(h, k)$
+- $x$-radius $a$
+- $y$-radius $b$
+- $\therefore \text{width}=2a, \quad \text{height}=2b$
+
+### Hyperbolas
+
+$${(x-h)^2 \over a^2} - {(y-k)^2 \over b^2} = 1$$
+
+- centre at $(h,k)$
+- asymptotes at $y-k=\pm{b \over a}(x-h)$
+
+${(x-h)^2 \over a^2} - {(y-k)^2 \over b^2} = 1$ and ${(y-k)^2 \over b^2} - {(x-h)^2 \over a^2} = 1$ are **conjugate hyperbolas**
+
+## Modulus function
+
+$$|x|=\sqrt{x^2}$$
+
+## Parametric equations
+
+### Circles
+$$\[\begin{cases}
+ x=a\cos t\\
+ y=a\sin t
+ \end{cases}
+\text{where radius} =a$$
+
+To convert to cartesian, factorise and use $\cos^2 x + \sin^2 x=1$
+
+$\cos^2 t + \sin^2 t = 1$
+$\implies {\cos^2 \over \sin^2 t} + {\sin^2 t \over sin^2 t} = {1 \over \sin^2 t} \implies \csc^2 t - \cot^2 t$