1. IB Math SL 1 Trigonometric Modelling Lesson Worksheet Name_____________
In this exercise, we are going to find an imperfect trig model for a real life situation, in the form:
f(x) = Asin[B(x – c1)] + d, and f(x) = Acos[B(x – c2)] + d
Note: x (and y) are the variables of theses equations. A, B, c1, c2 and d are the parameters of the equation.
Example: Average Daily Maximum Temperature in Cairo (in o
C)
t = 1 2 3 4 5 6 7 8 9 10 11 12
Month Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec
Temp 18.3 20.0 22.8 27.8 31.7 33.2 33.9 33.3 32.2 29.4 23.9 19.4
Step 1
x
y
: Label the scale, axes and plot the points:
Step 2
It should not go through all the points, because it is a model.
: Draw a sinusoidal function with a constant period/amplitude that best fits your points.
Step 3
x
y
: Translate your graph such that it looks like a standard sine graph:
Step 4: Find the period, and amplitude of your graph. Use P = 2π/B, B = 2π/P to find the value of B.
Step 5
This will give you your c1 and d values.
: Work out the translation required to translate the graph made in Step 3 into the one made in Step 2.
Step 6
mode. See if the points correspond to the values in the table above. Adjust your equation if necessary.
: Write out the equation of your function in the form f(x) = Asin[B(x – c1)] + d. Plot this function on your GDC in radian
Step 7
x
y
: Translate your graph in Step 2, such that it looks like a standard cosine graph:
Step 8
This will give you your c2 value. All other parameters should be the same.
: Work out the translation required to translate the graph made in Step 7 into the one made in Step 2.
Step 9
mode. See if the points correspond to the values in the table above. Adjust your equation if necessary.
: Write out the equation of your function in the form f(x) = Acos[B(x – c2)] + d. Plot this function on your GDC in radian
Step 10: Which values match up the best? Which values match up the worst?
2. Now complete the same exercise for Melbourne, Australia. Discuss which values match up the best and worst for your model.
Which model is closer to the formula, Melbourne or Cairo?
Example: Average Daily Maximum Temperature in Melbourne (in o
C)
t =
Month Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec
Temp 28.0 26.0 24.0 20.0 16.0 14.0 13.0 14.0 16.0 19.0 22.0 24.0
x
y
Space for working:
3. Another Trig Modelling Example
In the Bay of Borden, the difference between the high and low tides is 10m (fluctuates between 5m and –5m), and the average
time difference
:
between high and low tides is 14 hours. At 12 am, t = 0, and low tide occurs at 2am,
Step 1: Plot the above information on the axes below. Label the scale and axes:
x
y
Use the equation to find:
i) The approximate value for the level of the tide at 9pm.
Be careful about your value for t.
ii) The approximate value for the level of the tide at 6am the
following day. Be careful about your value for t.
HW Ex 13E #1, 2, 5, 6 (students should also find cosine models); IB Packet #2, 7
![IB Math SL 1 Trigonometric Modelling Lesson Worksheet Name_____________
In this exercise, we are going to find an imperfect trig model for a real life situation, in the form:
f(x) = Asin[B(x – c1)] + d, and f(x) = Acos[B(x – c2)] + d
Note: x (and y) are the variables of theses equations. A, B, c1, c2 and d are the parameters of the equation.
Example: Average Daily Maximum Temperature in Cairo (in o
C)
t = 1 2 3 4 5 6 7 8 9 10 11 12
Month Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec
Temp 18.3 20.0 22.8 27.8 31.7 33.2 33.9 33.3 32.2 29.4 23.9 19.4
Step 1
x
y
: Label the scale, axes and plot the points:
Step 2
It should not go through all the points, because it is a model.
: Draw a sinusoidal function with a constant period/amplitude that best fits your points.
Step 3
x
y
: Translate your graph such that it looks like a standard sine graph:
Step 4: Find the period, and amplitude of your graph. Use P = 2π/B, B = 2π/P to find the value of B.
Step 5
This will give you your c1 and d values.
: Work out the translation required to translate the graph made in Step 3 into the one made in Step 2.
Step 6
mode. See if the points correspond to the values in the table above. Adjust your equation if necessary.
: Write out the equation of your function in the form f(x) = Asin[B(x – c1)] + d. Plot this function on your GDC in radian
Step 7
x
y
: Translate your graph in Step 2, such that it looks like a standard cosine graph:
Step 8
This will give you your c2 value. All other parameters should be the same.
: Work out the translation required to translate the graph made in Step 7 into the one made in Step 2.
Step 9
mode. See if the points correspond to the values in the table above. Adjust your equation if necessary.
: Write out the equation of your function in the form f(x) = Acos[B(x – c2)] + d. Plot this function on your GDC in radian
Step 10: Which values match up the best? Which values match up the worst?](https://image.slidesharecdn.com/modelling-handout-150812133103-lva1-app6891/85/modelling-handout-1-320.jpg)
