Radians, Degrees, Arc Length, & Area of a Sector

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Presentation transcript:

Radians, Degrees, Arc Length, & Area of a Sector AS Maths with Liz Core 2

By the end of this lesson you will be able to… Convert between radians and degrees Work out the length of an arc Calculate the area of a given sector Find the area of a segment

So far in maths… you have measured angles in degrees However, angles can also be measured in radians. The symbol for this is

It’s almost an “equilateral arc” What is a radian? A radian is an angle measured based on the radius of a circle. One radian is defined by the angle at the centre of an arc where the arc length is the same as the radius. It’s almost an “equilateral arc”

Calculating 1c in degrees To calculate one radian, recall the arc length formula: Key Facts:

Example 1 – Converting between Degrees & Radians Convert the following (a) in radians (b) in degrees (c) in degrees (d) in radians

You try: Convert the following (a) in radians (b) in degrees (c) in degrees (d) in radians

Arc Length

Sector Area

Example 2

You try

Independent Study Core 2 textbook Pg. 389, Exercise 9A, #1 – 4 only DUE TUESDAY, JAN. 13TH Core 1 Past Paper – January 2012 (blue booklet) Please complete all questions on A4 paper Mark your work in colourful pen answers on moodle No gaps! (come to drop in for help) Correct any necessary DUE FRIDAY, JAN. 9TH