Modelling with Trigonometric Functions (AQA A-Level Mathematics): Quizzes

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Modelling with Trigonometric Functions
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What type of real-world behaviour are trigonometric functions ideal for modelling?

Periodic repeating phenomena

In y(t)=Asin(Bt+C)+Dy(t) = A \sin(Bt + C) + D, what does the parameter AA represent?

The amplitude

If the period is TT, which formula gives the value of BB in y(t)=Asin(Bt+C)+Dy(t) = A \sin(Bt + C) + D?

B=2πTB = \frac{2\pi}{T}

When should you use a sine function rather than cosine when modelling?

When starting at the midline

Given max value 20 and min value 4, what is the amplitude AA?

8

With max value 16 and min value 8, what is the vertical shift DD?

12

In the Ferris wheel example with 10m radius and base 2m above ground, what is DD?

12 metres

In the daylight hours example, if the period is 12 months, what is the value of BB?

π6\frac{\pi}{6}

What does the parameter CC represent in y(t)=Acos(Bt+C)+Dy(t) = A \cos(Bt + C) + D?

The phase shift

Which field uses trigonometric modelling for heartbeats and circadian cycles?

Biology

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