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
- 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"
Exam Tip
- 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
