Higher Engineering Mathematics, Sixth Edition
142 Higher Engineering Mathematics 0 y /2/ 3 /2 2 / t y 5 2 cos t y 5 2 cos(t 23 /10) 22 2 3 / 10 rads Figure 14.2 ...
Trigonometric waveforms 143 0 7 y (^908180827083608) A 8 y 5 7cos^2 2 A Figure 14.28 Now try the following exercise Exercise 62 ...
144 Higher Engineering Mathematics α, and a graph ofy=sin(ωt+α)leadsy=sinωtby angleα. (The angle ωt is measured in radians (i.e. ...
Trigonometric waveforms 145 (c) Whent=10ms thenv=340sin ( 50 π 10 103 − 0. 541 ) =340sin( 1. 0298 )=340sin59◦ =291.4V (d) Whenv= ...
146 Higher Engineering Mathematics reaches 3A. Sketch one cycle of the waveform showing relevant points. ⎡ ⎢ ⎢ ⎢ ⎢ ⎢⎢ ⎣ (a)5A,20 ...
Trigonometric waveforms 147 Voltage v (V) 0 30 230 250 2100 50 100 Time t (s) v 15 100 sin t 1 30 sin 3t 100 sin t 30 sin 3t ...
148 Higher Engineering Mathematics 0 4 24 210 10 T i 15 10 sin t 1 4 sin 2t 10 sin t 4 sin 2t 3 T 4 T 2 T 4 Current i (A) Ti ...
Trigonometric waveforms 149 Current i(A) 0 4 24 210 10 Time t (s) T i 25 10 sin t 1 4 sin( 2 t 1 2 ) 4 sin( 2 t 1 2 ) 10 ...
150 Higher Engineering Mathematics 339.4 Voltage v (V) 67.9 2 67.9 2 339.4 v 5 339.4 sin 100 t 1 67.9 sin( 300 t 2 34 ) 67.9 ...
Trigonometric waveforms 151 waveform using harmonic synthesis over one cycle of the fundamental waveform. ⎡ ⎢ ⎣ (a)v=300sin314. ...
Chapter 15 Trigonometric identities and equations 15.1 Trigonometric identities A trigonometric identityis a relationship that i ...
Trigonometric identities and equations 153 theright-handside(RHS)orvice-versa.It isoftenuseful to change all of the trigonometri ...
154 Higher Engineering Mathematics 2cos^2 A− 1 =cos^2 A−sin^2 A 4. cosx−cos^3 x sinx =sinxcosx ( 1 +cotθ)^2 +( 1 −cotθ)^2 =2c ...
Trigonometric identities and equations 155 1.0 2 1.0 2 0.6 (^09082708) 216.87 8 323.13 8 y 5 sin T S A C 908 1808 2708 3608 08 ...
156 Higher Engineering Mathematics In Problems 4 to 6, solve forθ in the range 0 ◦≤θ≤ 360 ◦. secθ=2[ 60 ◦, 300 ◦] cotθ= 0 .6[59 ...
Trigonometric identities and equations 157 15.6 Worked problems (iii)on trigonometric equations Problem 12. Solve the equation 8 ...
158 Higher Engineering Mathematics i.e. 18+18tan^2 A−3tanA− 21 = 0 18tan^2 A−3tanA− 3 = 0 Factorizing gives(6tanA− 3 )(3tanA+ 1 ...
Chapter 16 The relationship between trigonometric and hyperbolic functions 16.1 The relationship between trigonometric and hyper ...
160 Higher Engineering Mathematics But from Chapter 5, Problem 6, cosh^2 θ−sinh^2 θ= 1 , hence cos^2 jθ+sin^2 jθ=^1 Problem 2. V ...
The relationship between trigonometric and hyperbolic functions 161 But from equation (5), cosjA=coshA and from equation (6), si ...
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