Download presentation

Presentation is loading. Please wait.

Published byCarter Corcoran Modified over 3 years ago

1
RADIANS Definition An arc of length r subtends an angle of one radian at the centre of a circle of radius r r Ø=1radian

2
**Proof r How do you calculate the length of an arc? r = ø x 2πr 360º**

Ø=1radian How do you calculate the length of an arc? r = ø x 2πr 360º r = 1 radian x 2πr 360 º x 360 º 360r = 1 radian x 2πr ÷ r 360 º = 1 radian x 2π ÷ 2 180 º = 1 radian x π Or 180 º = π radians ÷ π 180 = 1 radian π so 1 radian is approximately…?

3
**Converting between angles and radians**

Degrees = radians x 180 π Radians = degrees x π 180 So if ø is measured in radians Then ø radians = ø x π 180

4
**How many different angles can you write as radians?**

2 180º = π radians

5
**Arc Length r Angle in degrees Arc length = ø x 2πr 360º**

Ø=1radian Angle in degrees Arc length = ø x 2πr 360º Arc length = 2πrø 360º Factorise r Arc length = r 2πø 360º Divide by 2 Angle in radians Arc length = r πø 180º Arc length = rø

6
**Area of Sector r Angle in degrees Sector area = ø x πr2 360º**

Ø=1radian Angle in degrees Sector area = ø x πr2 360º Sector area = πr2ø 360º Factorise r2 Sector area = r2 πø 360º Factorise out ½ Angle in radians Sector area = ½r2 πø 180º Sector area = ½r2ø

7
Examples Convert 50° into radians 50° = ° x π rad 180 50° = rad

8
**Examples Convert 2.7 radians into degrees 2.7 rad = 2.7 x 180 degrees**

π 2.7 rad = °

9
**Examples Convert 40° into radians 40° = 40 x π 180 40° = 40π 180**

40° = 40π 180 40° = 2π radians 9

10
**Calculate the arc length and sector area**

10cm 1.2radians Arc length = rө Arc length = 10 x 1.2 Arc length = 12cm Sector area = ½r2ө Area = ½ x 100 x 1.2 Area = 60cm2

Similar presentations

OK

Unit Circle. Special Triangles 30 60 Short Long Hypotenuse s s 2s Hypotenuse 45.

Unit Circle. Special Triangles 30 60 Short Long Hypotenuse s s 2s Hypotenuse 45.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on non biodegradable waste clip Ppt on carburetor working animation Ppt on earth and space lesson Ppt on end of life care Flexible oled display ppt on tv Ppt on adventure tourism in india Ppt on places in our neighbourhood clip Ppt on social contract theory example Ppt on kisan call centre Ppt on types of pollution in hindi