Sine & Cosine Formulae (Edexcel IGCSE Further Maths)

What is the sine formula?

• The sine formula allows us to find missing side lengths or angles in non-right-angled triangles
  • It is also known as the sine rule
• It states that for any triangle with angles A, B and C
  • 

• • • a is the side opposite angle A
    • b is the side opposite angle B
    • c is the side opposite angle C
• This formula is not on the exam formula sheet, so you need to remember it
• Remember that sin 90° = 1
  • So if one of the angles is 90° this becomes SOH from SOHCAHTOA

How can I use the sine formula to find missing side lengths or angles?

• The sine formula can be used when you have any opposite pairs of sides and angles
• Always start by labelling your triangle with the angles and sides
  • Remember
    • the sides with the lower-case letters
    • are opposite the angles with the equivalent upper-case letters
• Use the formula as given above to find the length of a side
• To find a missing angle it's easier to 'flip' the formula
  • 

• Substitute the values you have into the formula and solve
  • This will always give you an acute angle
  • If you know the angle is obtuse then subtract this value from 180

What is the cosine formula?

• The cosine formula allows us to find missing side lengths or angles in non-right-angled triangles
  
  • It is also known as the cosine rule
• It states that for any triangle
  • 

• • • a is the side opposite angle A
    • b and c are the other two sides
    • angle A is the angle in between sides b and c
• This formula is on the exam formula sheet
  • So you don't need to remember it
  • But you do need to be able to use it
• Remember cos 90° = 0
  • So if A = 90° this becomes Pythagoras’ Theorem

How can I use the cosine formula to find missing side lengths or angles?

• The cosine rule can be used when you have two sides and the angle between them or all three sides
• Always start by labelling your triangle with the angles and sides
  • Remember
    • the sides with the lower-case letters
    • are opposite the angles with the equivalent upper-case letters
• Use the formula in the formula sheet form to find an unknown side
• Rearrange the formula to find an unknown angle
  •  
    • Remember, A must be the angle in between sides b and c
• Substitute the values you have into the formula and solve

How do I find the area of a non-right-angled triangle?

• The area of any triangle can be found using the formula
  • 

• • • C is the angle in between sides a and b

• • This formula is not on the exam formula sheet, so you need to remember it
• Remember sin 90° = 1
  • so if C = 90° this becomes Area = ½ × base × height
• If you know the area you can use the formula to find the length of a side or an angle
  • Using inverse sin will always give you an acute angle
    • Subtract the value from 180 if you know the angle is obtuse