Arcs & Sectors Basic Definitions Calculating Arc Length Unit Assessment Level Questions Calculating Sector Area Course level questions.

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Arcs & Sectors Basic Definitions Calculating Arc Length Unit Assessment Level Questions Calculating Sector Area Course level questions

Definitions – Make sure you know these Angle Fraction Major and Minor Arcs & Arc Length The angle between two radii is critical in these calculations because the size of the angle is directly proportional to the arc length and the sector area. The angle is usually called  and the fraction of the circle formed by this angle is called the angle fraction it is Sectors & Sector Areas Angle Fraction Major and Minor Arcs & Arc Length An arc is a part of the circumference of a circle joining two points. Here the shorter arc joining A to B is the minor arc. The longer arc is the major arc. You will be expected to calculate the lengths of these arcs Sectors & Sector Areas The region enclosed by an arc and its two radii is called a sector. You need to be able to calculate such areas.

Calculating Arc Length These are very routine questions which you need to be able to work through quickly and accurately. The arc length formula lets you calculate the length IF you know the radius and the angle between the radii. The formula is: The arc length is this fraction Of the circumference =80° Example: calculate the minor arc length AB 7cm You will often find slight differences in rounding if you use the built in calculator value of .

Calculating Sector Area These are very routine questions which you need to be able to work through quickly and accurately. The sector area formula lets you calculate the area IF you know the radius and the angle between the radii. The formula is: The sector area is this fraction Of the circle area =80° Example: calculate the sector area shown 7cm

Unit Assessment Arcs/Sectors questions =65° Example: calculate the minor arc length AB 5.3m =65° Example: calculate the sector area shown 5.3m

Course Level Arcs/Sectors questions A circle has a segment removed as shown. The radius of the circle is 10 cm and the angle AOB = 60°. Calculate the area of the segment When solving these questions make sure you have a strategy and get used to the fact that you will have to make use of skills covered in other parts of the course Strategy, Notice that the triangle is equilateral and calculate its area. Calculate the area of the complete sector Subtract the triangle area to leave the segment area. Area of Equilateral Triangle is ½ bh = ½  5  5  3 = 25  3  2 (can you show why?) Area of Sector AB = 60  360  100  = 100  6 and collecting these together: