Higher Engineering Mathematics

122 GEOMETRY AND TRIGONOMETRY cosecant 321. 62 ◦= 1 sin 321. 62 ◦ =− 1. 6106 cotangent 263. 59 ◦= 1 tan 263. 59 ◦ = 0. 1123 Prob ...

INTRODUCTION TO TRIGONOMETRY 123 B (c) cot−^12. 1273 =tan−^1 ( 1 2. 1273 ) =tan−^10. 4700 ... =25.18◦or 25 ◦ 11 ′ or0.439 radian ...

124 GEOMETRY AND TRIGONOMETRY sin−^10. 2341 [ 13. 54 ◦,13◦ 32 ′, 0 .236 rad ] cos−^10. 8271 [ 34. 20 ◦,34◦ 12 ′, 0 .597 rad ...

INTRODUCTION TO TRIGONOMETRY 125 B a^2 =b^2 +c^2 − 2 bccosA or b^2 =a^2 +c^2 − 2 accosB or c^2 =a^2 +b^2 − 2 abcosC The rule may ...

126 GEOMETRY AND TRIGONOMETRY Case 1.P= 46 ◦ 27 ′,Q= 36 ◦,R= 97 ◦ 33 ′, p=36.5 mm andq= 29 .6 mm. From the sine rule: r sin 97◦ ...

INTRODUCTION TO TRIGONOMETRY 127 B Applying the sine rule: 32. 91 sin 64◦ = 25. 0 sinF from which, sinF= 25 .0 sin 64◦ 32. 91 = ...

128 GEOMETRY AND TRIGONOMETRY x=21 mm,y=34 mm,z=42 mm [ Z= 29 ◦ 46 ′,Y= 53 ◦ 30 ′, Z= 96 ◦ 44 ′, area=355 mm^2 ] 12.11 Practic ...

INTRODUCTION TO TRIGONOMETRY 129 B Figure 12.27 Applying the sine rule: PR sin 120◦ = PQ sinR from which, sinR= PQsin 120◦ PR = ...

130 GEOMETRY AND TRIGONOMETRY Figure 12.30 A laboratory 9.0 m wide has a span roof which slopes at 36◦on one side and 44◦on the ...

INTRODUCTION TO TRIGONOMETRY 131 B from which, sinB= AOsin 50◦ AB = 10 .0 sin 50◦ 30. 0 = 0. 2553 HenceB=sin−^10. 2553 = 14 ◦ 47 ...

132 GEOMETRY AND TRIGONOMETRY Calculate, correct to 3 significant figures, the co-ordinatesxandyto locate the hole centre atPsh ...

B Geometry and trigonometry 13 Cartesian and polar co-ordinates 13.1 Introduction There are two ways in which the position of a ...

134 GEOMETRY AND TRIGONOMETRY Figure 13.3 From Pythagoras’ theorem,r= √ 42 + 32 =5. By trigonometric ratios,α=tan−^134 = 36. 87 ...

CARTESIAN AND POLAR CO-ORDINATES 135 B (−5.4, 3.7) [ (6.55, 145. 58 ◦)or (6.55, 2.54 rad) ] (−7,−3) [ (7.62, 203. 20 ◦)or (7 ...

136 GEOMETRY AND TRIGONOMETRY Figure 13.9 which corresponds to lengthOAin Fig. 13.9. y=rsinθ= 4 .5 sin 5. 16 =− 4. 057 which cor ...

B Geometry and trigonometry 14 The circle and its properties 14.1 Introduction Acircleis a plain figure enclosed by a curved lin ...

138 GEOMETRY AND TRIGONOMETRY Problem 1. If the diameter of a circle is 75 mm, find its circumference. Circumference,c=π×diamete ...

THE CIRCLE AND ITS PROPERTIES 139 B (a) Since π rad= 180 ◦ then 1 rad= 180 ◦/π, therefore 0. 749 = 0. 749 ( 180 π )◦ = 42. 915 ◦ ...

140 GEOMETRY AND TRIGONOMETRY Since length of arc,s=rθthenθ=s/r Radius,r= diameter 2 = 42 2 =21 mm henceθ= s r = 36 21 = 1 .7143 ...

THE CIRCLE AND ITS PROPERTIES 141 B For example, Fig. 14.8 shows a circlex^2 +y^2 =9. More generally, the equation of a circle, ...