Radian Measure (Edexcel IAL Maths)

Spec point — 3.2

Radian measure

What are radians?

• Radians are an alternative to degrees for measuring angles

• 1 radian is the angle in a sector of radius 1 and arc length 1

• Radians are normally quoted in terms of π

• This leads to

  • 2π = 360°
  • π = 180°

• The symbol for radians is ^c but it is more usual to see rad

  • Often, when π is involved, no symbol is given as it is obviously in radians

• Radians are used in trigonometry (see Exact Values) and calculus (First Principles Differentiation – Trigonometry)

How do I convert between radians and degrees?

• The most common are below, these are helpful to know

• Multiples of these are quite common too, eg ¾π = 135°
• For less familiar angles use π = 180° to convert

How do I find the arc length of a sector with radians?

• The length of an arc is s = rθ

How do I find the area of a sector with radians?

• The area of a sector is A = ½r²θ

How do I solve sector problems with radians?

• Other angle, circle, area, etc skills may be needed
• For example, area of a triangle A = ½absinC

Exam Hint

• Exam papers will have a mixture of questions in degrees and radians

• Check the mode (degrees/radians) of your calculator before using it

• Ensure you know how to change the mode on your calculator

• For the Casio fx-991EX Classwiz

  • SHIFT then MENU SETUP
  • Choose option 2: ANGLE UNIT
  • Choose either 1: DEGREE or 2: RADIAN

Worked Example