Download presentation

Presentation is loading. Please wait.

Published byClinton Semmens Modified over 2 years ago

1
© Boardworks Ltd 2005 1 of 40 © Boardworks Ltd 2005 1 of 40 AS-Level Maths: Core 2 for Edexcel C2.5 Trigonometry 2 This icon indicates the slide contains activities created in Flash. These activities are not editable. For more detailed instructions, see the Getting Started presentation.

2
© Boardworks Ltd 2005 2 of 40 Contents © Boardworks Ltd 2005 2 of 40 The sine rule The cosine rule The area of a triangle using ½ ab sin C Degrees and radians Arc length and sector area Solving equations using radians Examination-style questions Arc length and sector area

3
© Boardworks Ltd 2005 3 of 40 Using radians to measure arc length Suppose an arc AB of a circle of radius r subtends an angle of θ radians at the centre. r r θ O A B where θ is measured in radians. If the angle at the centre is 1 radian then the length of the arc is r. If the angle at the centre is 2 radians then the length of the arc is 2 r. If the angle at the centre is 0.3 radians then the length of the arc is 0.3 r. In general: Length of arc AB = θr When θ is measured in degrees the length of AB is

4
© Boardworks Ltd 2005 4 of 40 Finding the area of a sector We can also find the area of a sector using radians. where θ is measured in radians. r r θ O A B Again suppose an arc AB subtends an angle of θ radians at the centre O of a circle. The angle at the centre of a full circle is 2 π radians. When θ is measured in degrees the area of AOB is In general: Area of sector AOB = r 2 θ Area of sector AOB = So the area of the sector AOB is of the area of the full circle.

5
© Boardworks Ltd 2005 5 of 40 Finding chord length and sector area A chord AB subtends an angle of radians at the centre O of a circle of radius 9 cm. Find in terms of π : a) the length of the arc AB. b) the area of the sector AOB. 9 cm O A B a) length of arc AB = θr = 6 π cm = 27 π cm 2 b) area of sector AOB = r 2 θ

6
© Boardworks Ltd 2005 6 of 40 Finding the area of a segment A chord AB divides a circle of radius 5 cm into two segments. If AB subtends an angle of 45° at the centre of the circle, find the area of the minor segment to 3 significant figures. 5 cm 45° O A B The formula for the area of a sector can be combined with the formula for the area of a triangle to find the area of a segment. For example: Let’s call the area of sector AOB A S and the area of triangle AOB A T.

7
© Boardworks Ltd 2005 7 of 40 Finding the area of a segment Now: Area of the minor segment = A S – A T = 9.8174… – 8.8388… = 0.979 cm 2 (to 3 sig. figs.) In general, the area of a segment of a circle of radius r is: where θ is measured in radians.

Similar presentations

OK

© Boardworks Ltd 20151 of 9 This icon indicates the slide contains activities created in Flash. These activities are not editable. For more detailed instructions,

© Boardworks Ltd 20151 of 9 This icon indicates the slide contains activities created in Flash. These activities are not editable. For more detailed instructions,

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on computer graphics 3d transformation Ppt on density based traffic light control system Appt only ph clinics Ppt on immunization schedule in india Ppt on column chromatography principle Ppt on nuclear family and joint family band Ppt on credit policy pdf Ppt on holographic technology hologram Marketing management ppt on jeans Ppt on linux shell scripting