The amplitude,
Trigonometry, MET2-NHT 2019 VCAA 2
The wind speed at a weather monitoring station varies according to the function
where
- What is the amplitude and the period of
? (2 marks)
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- What are the maximum and minimum wind speeds at the weather monitoring station? (1 mark)
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- Find
, correct to four decimal places. (1 mark)
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- Find the average value of
for the first 60 minutes, correct to two decimal places. (2 marks)
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A sudden wind change occurs at 10 am. From that point in time, the wind speed varies according to the new function
where
- Find the smallest value of
, correct to four decimal places, such that and are equal and are both increasing at 10 am. (2 marks)
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- Another possible value of
was found to be 31.4358 Using this value of
, the weather monitoring station sends a signal when the wind speed is greater than 38 km/h. i. Find the value of
at which a signal is first sent, correct to two decimal places. (1 mark)
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ii. Find the proportion of one cycle, to the nearest whole percent, for which
. (2 marks)
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- Let
and .
The transformationmaps the graph of onto the graph of . State the values of
, , and , in terms of where appropriate. (3 marks)
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Graphs, MET2-NHT 2019 VCAA 2 MC
The diagram below shows one cycle of a circular function.
The amplitude, period and range of this function are respectively
Graphs, MET1 SM-Bank 27
The graph shown is
- Write down the value of
. (1 mark)
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- Find the value of
. (1 mark)
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- Copy or trace the graph into your writing booklet.
On the same set of axes, draw the graph
for . (2 marks)
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Show Worked Solution
a.
b.
MARKER’S COMMENT: Graphs are consistently drawn too small by many students. Aim to make your diagrams 1/3 to 1/2 of a page.
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Functions, MET1 2006 VCAA 4
For the function
- write down the amplitude and period of the function. (2 marks)
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- sketch the graph of the function
on the set of axes below. Label axes intercepts with their coordinates.
Label endpoints of the graph with their coordinates. (3 marks)
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Show Answers Only
Show Worked Solution
a.
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Functions, MET1 2010 VCAA 4a
Write down the amplitude and period of the function
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Functions, MET1 2012 VCAA 6
The graphs of
- Find the value of
. (2 marks)
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- If
, find the -coordinate of the other point of intersection of the two graphs. (1 mark)
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Algebra, MET2 2014 VCAA 1
The population of wombats in a particular location varies according to the rule
- Find the period and amplitude of the function
. (2 marks)
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- Find the maximum and minimum populations of wombats in this location. (2 marks)
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- Find
. (1 mark)
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- Over the 12 months from 1 March 2013, find the fraction of time when the population of wombats in this location was less than
. (2 marks)
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