Phythagoras+Trigonometry - created from Mind Map

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Phythagoras Theorem

3D Phythagoras

Trigonometry

3D Trigonometry

Vectors

Only works for RIGHT-ANGLED TRIANGLES

Uses 2 sides to find the third side

Hypotenuse is longest side-Opposite is opposite angle-Adjacent is next to angle

Only for CUBOIDS

Calculating the longest diagonal

Can also be used for other shapes like square-based pyramid

Hypotenuse is longest side

Sine Rule

Cosine Rule

Opposite is opposite angle

SOH CAH TOA

Adjacent is next to angle being used

To use inverse=press 2nd Function followed with Sin/Cos/Tan

1. 2 angles given+any side

2. 2 sides given+an angle

SIDE HAS TO BE OPPOSITE ANGLE TO USE SINE RULE

1. 2 sides given+angle

2. All sides but no angle

SIDE DOES'NT HAVE TO BE OPPOSITE

1. Make a right-angled triangle between line+plane

2. Draw simple sketch of triangle+mark on lengths of sides, might have to use pythagoras first+then trig

For triangles inside 3D shapes thata re not right-angled, use Sine+Cosine rule

Vectors represent movement of a certain size in a certain direction

Multiplying vector by scalar

Adding/Subtracting vectors

Vectors along a straight line

Column vectors in brackets like coordinations

Represented by an arrow on a diagram

Exam questions use BOLD LETTERS/UNDERLINE LETTERS

Multiplying a vector by a positive number doubles the size of number but not direction

If number is negative then direction of arrow changes

a+b means 'go along a then b

c-d means 'go along c then backwards along d'

MINUS SIGN MEANS GO OPPOSITE WAY

To obtain unknown vectors just get around the diagram but any route, naming the vectors that you pass, either if you go backward a vector(negative)/forward a vector(positive)

Use vectors to show that points lie on a straight line

Vectors including ratios

If XYZ is a straight line, then XY,arrow pointing to right, must be a scalar multiple of YZ, arrow pointing to right

Ratios used to tell you lengths of different sections of a straight line

If XY : YZ = 2 : 3

Tells you that XY, arrow pointing to right, = 2 over 5 XZ, arrow pointing to right and YZ,arrow pointing to right= 3 over 5 XZ, arrow pointing to right