Higher Engineering Mathematics

142 GEOMETRY AND TRIGONOMETRY Problem 13. Sketch the circle given by the equation:x^2 +y^2 − 4 x+ 6 y− 3 =0. The equation of a c ...

THE CIRCLE AND ITS PROPERTIES 143 B The unit of angular velocity is radians per second (rad/s). An object rotating at a constant ...

144 GEOMETRY AND TRIGONOMETRY (a) Determine the angular velocity of the wheels in both rad/s and rev/min. (b) If the speed remai ...

THE CIRCLE AND ITS PROPERTIES 145 B Problem 17. An object is suspended by a thread 250 mm long and both object and thread move i ...

Assign-04-H8152.tex 23/6/2006 15: 7 Page 146 Geometry and trigonometry Assignment 4 This assignment covers the material containe ...

Assign-04-H8152.tex 23/6/2006 15: 7 Page 147 ASSIGNMENT 4 147 B h 60 ° 12 cm 12 cm Figure A4.2 portion, and (c) the area of the ...

Geometry and trigonometry 15 Trigonometric waveforms 15.1 Graphs of trigonometric functions By drawing up tables of values from ...

TRIGONOMETRIC WAVEFORMS 149 B 90 ° 360 ° 270 ° 0 0 ° 180 ° Quadrant 2 Quadrant 1 Y Quadrant 3 Quadrant 4 X AX Y      Fig ...

150 GEOMETRY AND TRIGONOMETRY (vii) In the first quadrant of Fig. 15.1 all the curves have positive values; in the second only s ...

TRIGONOMETRIC WAVEFORMS 151 B θ=tan−^11. 7629 = 60 ◦ 26 ′. Measured from 0◦, the two angles between 0◦and 360◦whose tangent is 1 ...

152 GEOMETRY AND TRIGONOMETRY Figure 15.10 Figure 15.11 graph, then asine waveis produced as shown in Fig. 15.10. If all horizon ...

TRIGONOMETRIC WAVEFORMS 153 B Figure 15.12 A graph ofy=sin 2Ais shown in Fig. 15.12. (ii) A graph ofy=sin^12 Ais shown in Fig. 1 ...

154 GEOMETRY AND TRIGONOMETRY Amplitude Amplitude is the name given to the maximum or peak value of a sine wave. Each of the gra ...

TRIGONOMETRIC WAVEFORMS 155 B whereαis a phase displacement compared with y=sinAory=cosA. (ii) By drawing up a table of values, ...

156 GEOMETRY AND TRIGONOMETRY Problem 11. Sketch y=2 cos(ωt− 3 π/10) over one cycle. Amplitude=2; period= 2 π/ωrad. 2 cos(ωt− 3 ...

TRIGONOMETRIC WAVEFORMS 157 B Figure 15.28 Now try the following exercise. Exercise 70 Further problems on sine and cosine curve ...

158 GEOMETRY AND TRIGONOMETRY by angleα, and a graph ofy=sin(ωt+α)leads y=sinωtby angleα. (The angle ωt is measured in radians ( ...

TRIGONOMETRIC WAVEFORMS 159 B (c)Whent=10 ms thenv=340 sin ( 50 π 10 103 − 0. 541 ) =340 sin(1.0298)=340 sin 59◦ =291.4 V (d) Wh ...

160 GEOMETRY AND TRIGONOMETRY current att=8 ms (d) the time when the cur- rent is first a maximum (e) the time when the current ...

TRIGONOMETRIC WAVEFORMS 161 B Figure 15.31 Figure 15.32 shown. If the negative half-cycle in Fig. 15.32 is reversed it can be se ...