Sketch graphs of trigonometric functions

Graphs of sin θ, cos θ and tan θ

Remember sin graph starts at 0

Amplitude and period transformations

Calculator to test answers: https://www.desmos.com/calculator

Solving triangles

Right Angled Triangles

Sine Rule 
Determine the sides




Determine the angles



Cosine Rule
Determine the sides



Determine the angles

Trig Ratios

30°, 45° and 60°

45°, 45°, 90° 

When you work with trig and radians, π means the same as 180° because 2π radians is a full circle 360°

Trig Ratios for positive multiples of

30°, 45° and 60°

Negative Multiples of 30°, 60° and 45° trig ratios 



Reduction Formulae 

Trigonometric identities

Identities 



Proving trigonometric identities



Solving trigonometric equations using identities

Trigonometric equations

Using CAST




Equations with multiple angles




Trigonometric equations that factorise




Solving a trigonometric equation by using reciprocal function




Make everything sin and cos

Trigonometric functions

Basic Trigonometry: Sin, Cos, Tan 



Relation between the trigonometric functions

Differential Calculus

Average gradient

Change in yChange in x

=△y△x

=y2−y1x2−x1

Limits




Limits from first principles



Differentiation
Differentiate from first principles



Rules of differentiation



Notation 




The gradient of a curve




Turning points

Intro to Differential Calculus

Functional notation, average gradient, limits, derivative from first principles and rules

Sketch graphs

Straight line




You can also let y=0 and calculate x to draw the line.

The Circle




The Ellipse




The Parabola




The Hyperbola


Solve simultaneous equations graphically

The Circle and the tangent

The equation of a circle

(x-a)² + (y-b)² = r²



The equation of a tangent

Equations of straight lines

Two point form





One point and a gradient (Point slope form)





The distance between two points

,



The midpoint of a line segment

,

Different forms of the Straight line

The Gradient(Slope)-intercept form

$y=mx+c$

Where m = gradient = difference in y divided by the difference in x





The Intercept form





http://www.vitutor.com/geometry/line/intercept_form.html

The General form

$ax+bx+c=0$
$\mathrm{<br>}$ $$

Angle between points is given

If you are given an angle (Θ) and you must determine the gradient: The tangent of the angle is the gradient of the line: tanΘ = m


The equation is given

$y=mx+c$
m is the gradient.

Two points are given

$m=\frac{y_2-<!--\; -\; -->y_1}{x_2-<!--\; -\; -->x_1}$



Parallel lines
If two lines are parallel, their gradients are the same.




Perpendicular lines
If two lines are perpendicular, their gradients are opposite and inverse of one another.

Manipulation of technical formulee

Rules for manipulating formulas 

1. What you do on the one side of the equal sign you must do on the other side.
2. If you must make an exponent the subject, you use logs.
3. The inverse operation of a 'root' is a 'power'.
   $\text{T}heinverseof\sqrt[3]{}is({)}^3$

Make u the subject of:

$v=u+atv-<!--\; -\; -->at=u\therefore <!--\; \therefore \; -->u=v-<!--\; -\; -->at$

Word problems

Also a good read: http://www.themathpage.com/alg/word-problems.htm

Linear equations

Linear equations

If the variable occurs more than once first simplify. The variables must all be taken to one side and then added or subtracted.

If the variable occurs in the denominator of a fraction, it must be removed. This is done by multiplying by the variable throughout the equation.

Simultaneous linear equations













Solving simultaneous equations (one linear and one quadratic)