Higher Engineering Mathematics, Sixth Edition
Chapter 13 The circle and its properties 13.1 Introduction Acircleisa plainfigureenclosed bya curved line,every point on which i ...
The circle and its properties 123 (xii) The angle at the centre of a circle, subtended by an arc, is double the angle at the cir ...
124 Higher Engineering Mathematics When s= whole circumference (= 2 πr) then θ= s r = 2 πr r = 2 π i.e. 2 πradians= 360 ◦ or πra ...
The circle and its properties 125 Area of sector Area of a sector= θ 360 (πr^2 )whenθis in degrees = θ 2 π (πr^2 )= 1 2 r^2 θ wh ...
126 Higher Engineering Mathematics Floodlit area=area of sector = 1 2 r^2 θ= 1 2 ( 55 )^2 ( 45 × π 180 ) =1188m^2 Problem 14. An ...
The circle and its properties 127 Determine the lengthof theradius and circum- ference of a circle if an arc length of 32.6cm s ...
128 Higher Engineering Mathematics 5 4 2 024 x y r^5 2 b 53 a 52 Figure 13.14 Comparing this with equation (2) gives: 2 e=− 2 a, ...
The circle and its properties 129 24 22 2 4 y 24 28 23 22 0 2 4 6 x r^5 4 Figure 13.16 which represents a circle,centre (2,−3)an ...
130 Higher Engineering Mathematics n= 1500 π rev/min= 1500 60 π =rev/s, then angular velocityω= 2 π ( 1500 60 π ) =50rad/s The l ...
The circle and its properties 131 r r (a) 5 t v 2 v 1 (b) V 2 v 1 v 2 v 2 2 Figure 13.17 Bisecting the angle betweenv 2 and ...
132 Higher Engineering Mathematics velocity,v= √ ( 2 .5gr)= √ ( 2. 5 )( 9. 8 )( 1500 ) = √ 36750 = 191 .7m/s and 191.7m/s= 191. ...
Revision Test 4 This Revision Test covers the material contained in Chapters 11 to 13.The marks for each question are shown in b ...
Chapter 14 Trigonometric waveforms 14.1 Graphs of trigonometric functions By drawing up tables of values from 0◦to 360◦, graphs ...
Trigonometric waveforms 135 curve appears to be discontinuous and repeats at intervals of 180◦. 14.2 Angles of any magnitude (i) ...
136 Higher Engineering Mathematics (vii) In the first quadrant of Fig. 14.1 all the curves have positive values; in the second o ...
Trigonometric waveforms 137 angles between 0◦and 360◦whose tangent is 1.7629 are 60 ◦ 26 ′and 180◦+ 60 ◦ 26 ′,i.e. 240 ◦ 26 ′. P ...
138 Higher Engineering Mathematics 1208 908 608 3608 3308 2 0.5 2 1.0 1.0 T 0.5 y R S S 9 T 9 y 5 sin x Angle x 8 308 608 1208 2 ...
Trigonometric waveforms 139 y 1.0 2 1.0 (^0) A° y 5 sin A y 5 sin 2A 90° 180° 270° 360° Figure 14.12 (ii) Agraphofy=sin^12 Aissh ...
140 Higher Engineering Mathematics Amplitude Amplitude is the name given to the maximum or peak value of a sine wave. Each of th ...
Trigonometric waveforms 141 (ii) By drawing up a table of values, a graph of y=sin(A− 60 ◦)may be plotted as shown in Fig. 14.20 ...
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