Higher Engineering Mathematics, Sixth Edition
102 Higher Engineering Mathematics (a) cot 17. 49 ◦= 1 tan17. 49 ◦ =3.1735 (b) cot 163◦ 52 ′= 1 tan163◦ 52 ′ = 1 tan163 52 ◦ 60 ...
Introduction to trigonometry 103 (c) cot−^12. 1273 =tan−^1 ( 1 2. 1273 ) =tan−^10. 4700 ... =25.18◦or 25 ◦ 11 ′ or0.439radians P ...
104 Higher Engineering Mathematics (a) cosecant 213◦ (b) cosecant 15. 62 ◦ (c) cosecant 311[◦ 50 ′ (a)− 1. 8361 (b) 3. 7139 (c) ...
Introduction to trigonometry 105 Evaluate correct to 5 significant figures: (a) cosec(− 143 ◦) (b) cot(− 252 ◦) (c) sec(− 67 ◦[ ...
106 Higher Engineering Mathematics Area of triangleXYZ =^12 (base) (perpendicular height) =^12 (XY)(XZ)=^12 ( 18. 37 )( 7. 906 ) ...
Introduction to trigonometry 107 Hence height of pylonAB =80tan23◦= 80 ( 0. 4245 )= 33 .96m =34m to the nearest metre. 80 m 23 ...
108 Higher Engineering Mathematics Now try the following exercise Exercise 48 Further problems on angles of elevation and depres ...
Introduction to trigonometry 109 (i)^12 ×base×perpendicular height, or (ii)^12 absinCor^12 acsinBor^12 bcsinA,or (iii) √ [s(s−a) ...
110 Higher Engineering Mathematics From the sine rule: r sin10◦ 27 ′ = 29. 6 sin36◦ from which, r= 29 .6sin10◦ 27 ′ sin36◦ =9.13 ...
Introduction to trigonometry 111 F= 136 ◦ 56 ′is not possible in this case since 136 ◦ 56 ′+ 64 ◦is greater than 180◦. Thus only ...
112 Higher Engineering Mathematics A section of the roof is shown in Fig. 11.30. B A 8.0 m C 338 408 Figure 11.30 Angle at ridge ...
Introduction to trigonometry 113 from which,length of tie, QR= 10 .0sin39◦ 44 ′ sin120◦ =7.38m Now try the following exercise Ex ...
114 Higher Engineering Mathematics 448 488 30.0 m D C B A Figure 11.36 For triangleABC, using Pythagoras’ theorem: BC^2 =AB^2 +A ...
Introduction to trigonometry 115 AngleOA′B′= 180 ◦− 120 ◦− 16 ◦ 47 ′= 43 ◦ 13 ′. Applying the sine rule: 30. 0 sin120◦ = OB′ sin ...
116 Higher Engineering Mathematics For the position shown determine the length ofACand the angle between the crank and the conne ...
Chapter 12 Cartesian and polar co-ordinates 12.1 Introduction There are two ways in which the position of a point in a plane can ...
118 Higher Engineering Mathematics From Pythagoras’ theorem,r= √ 32 + 42 =5 (note that −5 has no meaning in this context). By tr ...
Cartesian and polar co-ordinates 119 Now try the following exercise Exercise 53 Further problems on changing from Cartesian into ...
120 Higher Engineering Mathematics (Note that when changing from polar to Cartesian co-ordinates it is not quite so essential to ...
Cartesian and polar co-ordinates 121 two functions. They make changing from Cartesian to polar co-ordinates, and vice-versa, so ...
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