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MAS164:FundamentalsofMathematics StudyPeriod2,2024 ASSIGNMENT3 [12marks]Considerthetrigonometricfunction f ( t )=2+3sin(4 ? ( t ?1)). Whatistheamplitudeof f ( t )? [2marks] Whatistheperiodof f ( t )? [2marks] Whatarethemaximumandminimumvaluesattainedby
MAS164:FundamentalsofMathematics
StudyPeriod2,2024
ASSIGNMENT3
- [12marks]Considerthetrigonometricfunction f(t)=2+3sin(4?(t?1)).
- Whatistheamplitudeoff(t)? [2marks]
- Whatistheperiodoff(t)? [2marks]
- Whatarethemaximumandminimumvaluesattainedbyf(t)? [4marks]
- Sketchthegraphoff(t)fort?[?1,1]. [4marks] [12marks]A water wave in a lake has a frequency of 20 Hz (i.e.,a wavelength or period of0.05 seconds).Within each wave, the water level reaches a maximum height of 2.5 meters anda minimum height of 0.5 meters.Supposing that t=0 corresponds to the water level at its minimum height, write down a trigonometric function that describes this water wave.Sketch the water wave over two periods.(Hint: Since the period = 0.05 seconds, which is very small, make the scale on the horizontal axis really big when you sketch the graph).
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