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Cogito

Trigonometry · Chapter 6 · Lesson 3

Practice Worksheet

Modelling with Sinusoids

Fit a wave to something that actually repeats.

12 problems · about 22 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 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, min 10. What is the amplitude?

    Answer

  2. Data starts at its maximum. Which model avoids a phase shift?

    • Cosine, because it starts at its peak.
    • Sine, because it starts at zero.

  3. Max 20, min 4. Amplitude?

    Answer

  4. Max 20, min 4. Midline?

    Answer

  5. The 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. What is the maximum?

    Answer

  2. h = 5 sin(60t) + 9. What is the period, in units of t?

    Answer

  3. A wheel runs between 1 m and 31 m. What is the midline, in metres?

    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. h = −20 cos(45t) + 22. What is the height at t = 0, in metres?

    Answer

  3. The Tide

    High tide is 6 m and low tide is 2 m. What is the amplitude?

    Answerm

  4. The Daylight

    Daylight runs between 9 and 15 hours over a year. What is the midline, in hours?

    Answerhours