Edexcel IGCSE Maths 复习笔记 4.13.1 Circles - Sector Areas & Arc Lengths

What is a sector? What is an arc?

• A maths book will (correctly) tell you that an arc is part of the circumference of a circle and a sector is part of a circle enclosed by two radii (radiuses) and an arc
• It’s much easier to think of a sector as the shape of a slice of a circular pizza (or cake, or pie, or …) and an arc as the curvy bit at the end of it (where the crust is)

• If the angle of the slice is θ (that’s the Greek letter “theta”) then the formulas for the area of a sector and the length of an arc are just fractions of the area and circumference of a circle:

• If you are not too good at remembering formulae there is a logic to these two
• You’ll need to remember the circumference and area formulas
• After that we are just finding a fraction of the whole circle – “θ out of 360”
• Other than that, working with sector and arc formulas is just like working with any other formula:

1. WRITE DOWN – what you know (what you want to know)
2. Pick correct FORMULA
3. SUBSTITUTE and SOLVE