Cycle 2 - Lesson 6 – Part II – Modelling with Trigonometric Functions Steps to modeling a sinusoidal (sine or cosine) function: Step 1: Determine the horizontal axis. (Max + Min) / 2 The equation of the axis is y = c Step 2: Determine the amplitude a = (Max – Min) / 2 Step 3: Determine the period (time to complete 1 cycle) and the k value. Step 4: Determine the phase shift by finding the “starting point” of the function
y = sin x
y = cos x
MODELLING DATA – Desmos activity The variation in maximum daily temperatures in a northern ontario town over one year is shown. Month 1 is January and Month 12 is December. Use Desmos to help you model a sinusoidal function for this data.
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FERRIS WHEEL Passengers on the London Eye ferris wheel board their pod at the bottom of the circle at a height of 5 metres above the ground. One full rotation takes 32 minutes and passengers reach a maximum height of 135 metres. a) Model the height of a passenger over time using a sine function AND a cosine function. Possible Sine function
Diagram of wheel
Possible Cosine function
Labelled sketch of sine function
b) At what times is a rider at a height of 120 metres?
c) Which parameter(s) would change if the entire wheel were raised up by 7 metres?
d) What is the radius of this wheel? Which parameter does the radius correspond to?
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MORE PRACTICE with APPLICATIONS of Trig functions 1.
Part II - Modelling and Applications of Trigonometric Functions.pdf
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