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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.

2.

3.

4.

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5.

Answers to More practice with Applications 1.

3.

2.

4.

5.

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MORE PRACTICE with Modelling Sinusoidal Functions

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