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Edexcel A Level Maths: Pure:复习笔记5.4.1 Radian Measure
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Date: 2022年10月31日 上午9:58
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"
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
转载自savemyexams
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