IB DP Maths: AA SL復習筆記3.5.3 Modelling with Trigonometric Functions
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.
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