Geometry and Trigonometry

Formula Booklet

Part if Topic Name Equation
3.1

Length of arc

l=θr

Area of sector

A=12θr2

3.2 Trigonometric identity tanθ=sinθcosθ
3.3

Pythagorean identity

cos2θ+sin2θ=1

Double angle formulae

sin2θ=2sinθcosθcos2θ=cos2θ-sin2θ           =2cos2θ-1           =1-sin2θ

3.6

Cosine rule

c2=a2+b2-2abcosCcosC=a2+b2+c22ab

Sine rule

asinA=bsinB=csinC

Area of triangle

A=12absinC

Basics and Main rules

Triangles


Soh Cah Toa  =
sinθ = oppositehypotenuse = ac
cosθ=adjacenthypotenuse=bc
tanθ  =   oppositeadjacent  =  ab

Example question

Find side a:

Question Solution
Find side a, when LA is 62° and side b is 8
  1. tanθ=oppositeadjacent
  2. tan(62)=a8
  3. a=tan(62)×8
  4. a=15.05
  1. Identify the appropriate equation
  2. Input the values
  3. Rearrange
  4. Calculate

 

Sine rule

asinA=bsinB=csinC sinAa=sinBb=sinCc

Used when you know 3 out of these values - asinA=bsinB

Example question

Question Solution
Find LB, when side a is 2 and c is 3
  1. sinAa=sinBb
  2. sin(28.9)3=sinB4
  3. B=sin-1(4×sin(28.9)3)
  4. B=40.12
  1. Identify the appropriate equation
  2. Input the values
  3. Rearrange
  4. Calculate

 

Cosine rule

c2=a2+b2-2abcosC cosC=a2+b2-c22ab

Used when you know 3 out of these values - c2=a2+b2-2abcosC

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Example question

Question Solution
Find side c, when LC is 46.6, side a is 2 and side b is 4
  1. c2=a2+b2-2abcosC
  2. c2=22+42-2×2×4×cos(46.6)
  3. c=22+42-2×2×4×cos(46.6)
  4. c=3.00
  1. Identify the appropriate equation
  2. Input the values
  3. Rearrange
  4. Calculate

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