CIE A Level Maths: Pure 1复习笔记3.3.1 Radian Measure

Radian measure

• 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 change 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 use radians to find the length of an arc?

• The length of an arc is s = rθ

How do I use radians to find the area of a sector?

• The area of a sector is A = ½θr²

Solving problems with radians

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