Basic Engineering Mathematics, Fifth Edition

188 Basic Engineering Mathematics Evaluate, correct to 4 decimal places, 4 .5cos67◦ 34 ′−sin90◦ 2tan45◦ Evaluate, correct to 4 ...

Introduction to trigonometry 189 cos38◦= QR PR = 7. 5 PR ,hence PR= 7. 5 cos38◦ = 7. 5 0. 7880 =9.518cm Check: using Pythagoras’ ...

190 Basic Engineering Mathematics 598 (d) x 4.30 438 x (e) 6.0 (f) 538 x 7.0 Figure 21.24 Findtheunknownsidesandanglesintherigh ...

Introduction to trigonometry 191 A ladder rests against the top of the perpendi- cular wall of a building and makes an angle of ...

192 Basic Engineering Mathematics From equation (2), height of building, h= 1. 0724 x= 1. 0724 ( 56. 74 )=60.85m. Problem 25. Th ...

Revision Test 8 : Angles, triangles andtrigonometry This assignment covers the material contained in Chapters 20 and 21.The mark ...

194 Basic Engineering Mathematics In Figure RT8.7, determine anglesx,yandz. (3) 598 y z x 378 Figure RT8.7 In Figure RT8.8, d ...

Chapter 22 Trigonometric waveforms 22.1 Graphs of trigonometric functions Bydrawinguptablesofvaluesfrom0◦to 360◦, graphs ofy=sin ...

196 Basic Engineering Mathematics 22.2 Angles of any magnitude Figure 22.2 shows rectangular axesXX′ and YY′ intersecting at ori ...

Trigonometric waveforms 197 A knowledge of angles of any magnitude is needed when finding, for example, all the angles between 0 ...

198 Basic Engineering Mathematics S 1808 2708 08 3608 908 T A C   Figure 22.10 Cosine is positive in the first and fourth quad ...

Trigonometric waveforms 199 2 0.5 0.5 2 1.0 1.0 y S R T S^9 O 9 y 5 cosx Angle x 8 308 608 1208 1808 2408 3008 3608 458 15808 33 ...

200 Basic Engineering Mathematics y 1.0 1.0 0 90  180  270  360 A ysin 3A Figure 22.14 y 0 90  180  270  360  x  4 ...

Trigonometric waveforms 201 908 2708 y (^0) A 8 2 1.0 1.0 y^5 sin (A^2608 ) y 5 sin A 608 608 1808 3608 Figure 22.18 1808 458 (^ ...

202 Basic Engineering Mathematics Now try the following Practice Exercise PracticeExercise 88 Trigonometric waveforms (answers o ...

Trigonometric waveforms 203 hence,^0.^90 =^2 .5sin(^0 +α) i.e. sinα=^0.^90 2. 5 = 0. 36 Hence, α=sin−^10. 36 = 21. 10 ◦ = 21 ◦ 6 ...

204 Basic Engineering Mathematics v=300sin( 200 πt− 0. 412 )V A sinusoidal voltage has a maximum value of 120V and a frequency ...

Chapter 23 Non-right-angled triangles and some practical applications 23.1 The sine and cosine rules To ‘solve a triangle’ means ...

206 Basic Engineering Mathematics or (b) 1 2 absinCor 1 2 acsinBor 1 2 bcsinA or (c) √ [s(s−a)(s−b)(s−c)]wheres= a+b+c 2 23.3 Wo ...

Non-right-angled triangles and some practical applications 207 TrianglePQRis shown in Figure 23.4. q 5 29.6mm p 5 36.5mm 368 r Q ...