Basic Engineering Mathematics, Fifth Edition

Revision Test 9 : Trigonometric waveforms and practicaltrigonometry

This assignment covers the material contained in Chapters 22–24.The marks available are shown in brackets at the
end of each question.

1. A sine wave is given byy=8sin4x. State itspeak
   value and its period, in degrees. (2)


2. A periodic function is given by y=15tan2x.
   State its period in degrees. (2)


3. The frequency of a sine wave is 800Hz. Calculate
   the periodic time in milliseconds. (2)


4. Calculate the frequency of a sine wave that has a
   periodic time of 40μs. (2)


5. Calculate the periodic time for a sine wave having
   a frequency of 20kHz. (2)


6. An alternating current completes 12 cycles in
   16ms. What is its frequency? (3)


7. A sinusoidal voltage is given by
   e=150sin( 500 πt− 0. 25 )volts. Determine the
   (a) amplitude,
   (b) frequency,
   (c) periodic time,
   (d) phase angle (stating whether it is leading or
   lagging 150sin500πt). (4)


8. Determinetheacuteanglesindegrees,degreesand
   minutes, and radians.
   (a) sin−^10 .4721 (b) cos−^10. 8457
   (c) tan−^11. 3472 (9)


9. Sketch the following curves, labelling relevant
   points.
   (a) y=4cos(θ+ 45 ◦) (b) y=5sin( 2 t− 60 ◦)
   (8)


10. The current in an alternating current cir-
    cuit at any time t seconds is given by
    i=120sin( 100 πt+ 0. 274 )amperes. Determine
    (a) the amplitude, frequency, periodic time and
    phase angle (with reference to 120sin100πt),
    (b) the value of current whent=0,
    (c) the value of current whent=6ms.
    Sketch one cycle of the oscillation. (16)


11. A triangular plot of land ABC is shown in
    Figure RT9.1. Solve the triangle and determine
    its area. (10)

A

B

C

15 m

15.4 m

718

Figure RT9.1

12. A car is travelling 20m above sea level. It then
    travels 500m up a steady slope of 17◦. Determine,
    correct to the nearest metre, how high the car is
    now above sea level. (3)


13. Figure RT9.2 shows a roof trussPQRwith rafter
    PQ=3m. Calculate the length of
    (a) the roof risePP′,
    (b) rafterPR,
    (c) the roof spanQR.
    Find also (d) the cross-sectional area of the roof
    truss. (11)

P

Q P 9 R

3m

408 328

Figure RT9.2

14. Solve triangleABCgivenb=10cm,c=15cm
    and∠A= 60 ◦. (10)


15. Change the following Cartesian co-ordinates into
    polar co-ordinates, correct to 2 decimal places, in
    both degrees and in radians.
    (a) (− 2. 3 , 5. 4 ) (b)( 7. 6 ,− 9. 2 ) (10)


16. Change the following polar co-ordinates into
    Cartesian co-ordinates, correct to 3 decimal
    places.
    (a) ( 6. 5 , 132 ◦) (b)( 3 ,3rad) (6)