boylistad

SECTION 13.3 The Sine Wave
11. Convert the following degrees to radians:
a. 45° b. 60°
c. 120° d. 270°
e. 178° f. 221°
12. Convert the following radians to degrees:
a. p/4 b. p/6
c. � 1
10
�p d. � 7
6 �p
e. 3p f. 0.55p
13. Find the angular velocity of a waveform with a period of
a. 2 s. b. 0.3 ms.
c. 4 ms. d. � 1
26
� s.
14. Find the angular velocity of a waveform with a frequency
of
a. 50 Hz. b. 600 Hz.
c. 2 kHz. d. 0.004 MHz.
15. Find the frequency and period of sine waves having an
angular velocity of
a. 754 rad/s. b. 8.4 rad/s.
c. 6000 rad/s. d. � 1
16
� rad/s.
16. Given f � 60 Hz, determine how long it will take the
sinusoidal waveform to pass through an angle of 45°.
17. If a sinusoidal waveform passes through an angle of 30°
in 5 ms, determine the angular velocity of the waveform.
SECTION 13.4 General Format for the Sinusoidal
Voltage or Current
18. Find the amplitude and frequency of the following
waves:
a. 20 sin 377t b. 5 sin 754t
c. 10 6 sin 10,000t d. 0.001 sin 942t
e. �7.6 sin 43.6t f. ( � 1
4
2 �) sin 6.283t
19. Sketch 5 sin 754t with the abscissa
a. angle in degrees.
b. angle in radians.
c. time in seconds.
20. Sketch 10 6 sin 10,000t with the abscissa
a. angle in degrees.
b. angle in radians.
c. time in seconds.
21. Sketch �7.6 sin 43.6t with the abscissa
a. angle in degrees.
b. angle in radians.
c. time in seconds.
22. If e � 300 sin 157t, how long (in seconds) does it take
this waveform to complete 1/2 cycle?
23. Given i � 0.5 sin a, determine i at a � 72°.
24. Given v � 20 sin a, determine v at a � 1.2p.
*25. Given v � 30 � 10 �3 sin a, determine the angles at
which v will be 6 mV.
*26. If v � 40 V at a � 30° and t � 1 ms, determine the
mathematical expression for the sinusoidal voltage.
PROBLEMS ⏐⏐⏐ 567