By K. A. Stroud

ISBN-10: 0333123352

ISBN-13: 9780333123355

ISBN-10: 134915394X

ISBN-13: 9781349153947

Because the book of the 3rd variation of "Engineering Mathematics", massive adjustments in syllabuses and thoughts for a degree skills in arithmetic were brought nationally, because of which scholars with a number of degrees of mathematical history were enrolling for undergraduate classes in engineering and technology. those alterations have result in the necessity for studying fabrics aimed toward diverse degrees. this article hence contains ten programmes which act as an creation to "Engineering arithmetic" and is designed for these scholars forthcoming the topic for the 1st time.

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**Sample text**

We already know that to simplify ; : ~: we first obtain a denominator that is entirely real by multiplying top and bottom by ...................... e. 3 - j4 DDDDOODOOOOOOOOOODOOODDDDDDDDDODDDDDDD Right. [(cos e. cos 82 +sin e. sin 82) + j(sin e. cos 82- cos e. sin 82)] r2 1 = 71 [cos ( 81 - 8 2) + j sin(8 1 ,2 - 8 2)] So, for division, the rule is .......................... 18 divide the r's and subtract the angle DOODOODDDDDDDDDODDDDDDDDDDDODDDDDDDDDD That is correct. g. o . o 6(cos 72° + j sin 72°) _ 2(cos 41 o + j sin 41 o)- 3(cos 31 + JSlll 31 ) So we now have two important rules Ifzt =rt(cosOt +j sin8t)andz 2 =r2 (cos8 2 +j sin8 2) then (i) ZtZ 2 = '•'2 [cos(8.

And .......... 6 ODDDDDDODDODDDODDDDDDDDDDDDODODDDDDDOD Now let us consider the following example. First the diagram. Express z = 4- j3 in polar form. From this, y r=5 tan E =~ =0-75 :. E = 36°52' 8 = 360°- 36°52' = 323°81 v, z = 4- j3 = 5( cos 323°81 + j sin 323°8') or in shortened form, z = ................... ,-- --- x - j Y1 But the direction of the vector, measured from OX, could be given as -36°52', the minus sign showing that we are measuring the angle in the opposite sense from the usual positive direction.

4 X 3 X 2) [cos(20° + 30° + 40°) + j sin(20° + 30° + 40°)] = 24( cos 90° + j sin 90°) DDDDODDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD Now what about a few revision examples on the work we have done so far? Turn to the next frame. 46 Programme 2 21 Revision Exercise Work all these questions and then turn on to frame 22 and check your results. 1. Express in polar form, z =-4 + j2. 2. Express in true polar form, z =5( cos 55°-j sin 55°) 3. ) 10(cos 126° + j sin 126°) 11 2(cos72° +jsin72°) 4. Express in the form a+ jb, (i) 2( cos 30° + j sin 30°) (ii) 5( cos 57° - j sin 57°) Solutions are on frame 22.

### Engineering Mathematics: Programmes and Problems by K. A. Stroud

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