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Cogito

Integrated Math 3 · Chapter 5 · Lesson 3

Practice Worksheet

Modelling Periodic Phenomena

Fitting a wave to something that repeats.

12 problems · about 21 minutes · F-TF.B.5, F-IF.B.4

NameDate

Figure — use these to answer the problems

Set amplitude and cycles to match a description, then read off the peak and trough.
-8-8-6-6-4-4-2-222446688
y = 2 sin(1x) + 0
a, amplitude2
b, cycles1
c, shift0
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. Max 30 and min 10. What is the amplitude?

    Answer

  2. Data starts at its minimum. What model avoids a phase shift?

    • A negative cosine, which starts at its lowest point.
    • A positive sine.

  3. Max 20, min 4. Amplitude?

    Answer

  4. Max 20, min 4. Midline?

    Answer

  5. A cycle takes 12 hours. What is b, in degrees per hour?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. h = 5 sin(60t) + 9. Maximum value?

    Answer

  2. h = 5 sin(60t) + 9. Period in units of t?

    Answer

  3. h = −20 cos(45t) + 22 at t = 0. What is h?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Put the modelling steps in order.

    Write 1 to 4 in the boxes to put these in order.

    • Find the midline from the average of max and min.
    • Find the amplitude from half the gap.
    • Find b from 360 divided by the period.
    • Choose sine or cosine from where the data starts.

  2. A wheel runs between 1 m and 31 m. Midline in metres?

    Answer

  3. The Amplitude

    Max 42 and min 2. What is the amplitude?

    Answer

  4. The Value of b

    A cycle takes 8 minutes. What is b, in degrees per minute?

    Answer