Phythagoras+Trigonometry

Phythagoras+Trigonometry

1. Phythagoras Theorem

   • 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

2. 3D Phythagoras

   • Only for CUBOIDS
     • Calculating the longest diagonal
       • Can also be used for other shapes like square-based pyramid

3. Trigonometry

   • Hypotenuse is longest side
     • Opposite is opposite angle
       • Adjacent is next to angle being used
         • To use inverse=press 2nd Function followed with Sin/Cos/Tan
     • SOH CAH TOA
   • Sine Rule
     • 1. 2 angles given+any side
       • 2. 2 sides given+an angle
         • SIDE HAS TO BE OPPOSITE ANGLE TO USE SINE RULE
   • Cosine Rule
     • 1. 2 sides given+angle
       • 2. All sides but no angle
         • SIDE DOES'NT HAVE TO BE OPPOSITE

4. 3D Trigonometry

   • 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

5. Vectors

   • Vectors represent movement of a certain size in a certain direction
     • Column vectors in brackets like coordinations
       • Exam questions use BOLD LETTERS/UNDERLINE LETTERS
     • Represented by an arrow on a diagram
   • Multiplying vector by scalar
     • Multiplying a vector by a positive number doubles the size of number but not direction
       • If number is negative then direction of arrow changes
   • Adding/Subtracting vectors
     • 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)
   • Vectors along a straight line
     • Use vectors to show that points lie on a straight line
       • If XYZ is a straight line, then XY,arrow pointing to right, must be a scalar multiple of YZ, arrow pointing to right
     • Vectors including ratios
       • 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