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IB DP Maths: AA SL复习笔记3.5.3 Modelling with Trigonometric Functions
Category:
IB课程
,
教材笔记
,
福利干货
Date: 2022年7月18日 上午11:28
Modelling with Trigonometric Functions
What can be modelled with trigonometric functions?
Anything that oscillates (fluctuates periodically) can be modelled using a trigonometric function
Normally some transformation of the sine or cosine function
Examples include:
Notice that the x-axis will not always contain an angle
In the examples above time or number of days would be on the x-axis
Depth of the water, temperature or vertical height would be on the y-axis
What are the parameters of trigonometric models?
A
trigonometric model
could be of the form
The bigger the value of
b
the quicker the function repeats a cycle
The
c
represents the
horizontal shift
The
d
represents the
vertical shift
This is the
principal axis
What are possible limitations of a trigonometric model?
The amplitude is the same for each cycle
In real-life this might not be the case
The function might get closer to the value of
d
over time
The period is the same for each cycle
In real-life this might not be the case
The time to complete a cycle might change over time
Exam Tip
The variable in these questions is often
t
for time.
Read the question carefully to make sure you know what you are being asked to solve.
Worked Example
a) Write down the depth of the water at midnight.
b) Find the minimum water depth and the number of hours after midnight that this depth occurs.
c) Calculate how long the water depth is at least 13.5 m each day.
转载自savemyexams
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