Higher Engineering Mathematics, Sixth Edition
162 Higher Engineering Mathematics cosAsinB= 1 2 [sin(A+B)−sin(A−B)] ⎡ ⎢ ⎣ coshθcoshφ= 1 2 [sinh(θ+φ) −sinh(θ−φ)] ⎤ ⎥ ⎦ sin^3 ...
Chapter 17 Compound angles 17.1 Compound angle formulae An electric current i maybeexpressedasi= 5sin(ωt− 0. 33 )amperes. Simila ...
164 Higher Engineering Mathematics tan ( x+ π 4 ) = tanx+tanπ 4 1 −tanxtanπ 4 from the formula fortan(A+B) = tanx+ 1 1 −(tanx)( ...
Compound angles 165 Show that: (a) sin ( x+ π 3 ) +sin ( x+ 2 π 3 ) = √ 3cosx and (b)−sin ( 3 π 2 −φ ) =cosφ Prove that: (a) ...
166 Higher Engineering Mathematics There is only one quadrant where both sinαandcosα are positive, and this is the first, as sho ...
Compound angles 167 R 2 7.3 4.6 Figure 17.4 Problem 8. Express−2.7sinωt− 4 .1cosωtin the formRsin(ωt+α). Let−2.7sinωt− 4 .1cos ...
168 Higher Engineering Mathematics i.e. θ+ 59. 03 ◦= 43. 32 ◦or 136. 68 ◦ Hence θ= 43. 32 ◦− 59. 03 ◦=− 15. 71 ◦ or θ= 136. 68 ◦ ...
Compound angles 169 Solve the following equations for values of θ√between 0◦and 360◦:(a)6cosθ+sinθ= 3(b)2sin3θ+8cos3θ=1. ⎡ ⎣ ( ...
170 Higher Engineering Mathematics LHS= 1 −cos2θ sin2θ = 1 −( 1 −2sin^2 θ) 2sinθcosθ = 2sin^2 θ 2sinθcosθ = sinθ cosθ =tanθ=RHS ...
Compound angles 171 (iv) cos(A+B)−cos(A−B)=−2sinAsinB i.e. sinAsinB =−^12 [cos(A+B)−cos(A−B)] (4) Problem 15. Express sin4xcos3x ...
172 Higher Engineering Mathematics Solving the simultaneous equations gives: A= X+Y 2 andB= X−Y 2 Thus sin(A+B)+sin(A−B)=2sinAco ...
Compound angles 173 In Problems 7 and 8, solve forθin the range 0◦≤ θ≤ 180 ◦. cos6θ+cos2θ= 0 [22. 5 ◦, 45 ◦, 67. 5 ◦, 112. 5 ◦, ...
174 Higher Engineering Mathematics 2 (^0) t (seconds) v p i p i v 1 2 Figure 17.9 The waveforms ofv,iandpare shown in Fi ...
Compound angles 175 2 (^0) t (seconds) v p i p i v 1 2 Figure 17.10 p i v v p i 0 1 2 ^2 t (seconds) Figure 17.11 ...
176 Higher Engineering Mathematics pulsate at twice the supply frequency. The areas of the power curve (shown shaded) above the ...
Revision Test 5 This Revision Test covers the material contained in Chapters 14 to 17.The marks for each question are shown in b ...
Chapter 18 Functions and their curves 18.1 Standard curves When a mathematical equation is known, co-ordinates may be calculated ...
Functions and their curves 179 The simplest example of a cubic graph,y=x^3 ,is shown in Fig. 18.3. 8 y^5 x^3 6 4 2 22 24 26 28 2 ...
180 Higher Engineering Mathematics x^2 y^2 a^2 b^2 1 51 y C b O a D x A B Figure 18.7 In the above equation, ‘a’ is the semi-maj ...
Functions and their curves 181 0 1 y 5 ex y x Figure 18.11 O a a r 5 a sin Figure 18.12 18.2 Simple transformations From the gr ...
«
5
6
7
8
9
10
11
12
13
14
»
Free download pdf