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Cogito

Trigonometry · Chapter 3 · Lesson 2

Practice Worksheet

Period and Phase Shift

The coefficient inside squeezes; the number inside slides.

12 problems · about 22 minutes · F-TF.B.5, F-IF.C.7

NameDate

Figure — use these to answer the problems

Change b and count the cycles. Change c and watch the whole wave slide.
-8-8-6-6-4-4-2-222446688
y = 1 sin(2x) + 0
a, amplitude1
b, cycles2
c, shift0
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. y = cos(3x). What is the period, in degrees?

    Answer

  2. In y = sin(2x − 80°), what is the phase shift in degrees?

    Answer

  3. y = sin(2x). Period in degrees?

    Answer

  4. y = cos(6x). Period in degrees?

    Answer

  5. y = sin(x − 40°). Phase shift in degrees, right being positive?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. y = sin(3x − 60°). Phase shift in degrees?

    Answer

  2. y = 5 sin(2x) + 3. Maximum value?

    Answer

  3. A wheel turns once every 20 seconds. What is b if t is in seconds and the model uses degrees?

    Answer

Stretch Yourself

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

4 problems

  1. Sort each change by whether it moves the graph horizontally or vertically.

    Write each item under the heading it belongs to: The b in sin(bx) · The c in sin(x − c) · The a in a sin x · The d in sin x + d

    Horizontal

    Vertical

  2. y = sin(0.5x). Period in degrees?

    Answer

  3. The Period

    y = sin(4x). What is the period, in degrees?

    Answerdegrees

  4. The Tide

    A tide is modelled by y = 2 sin(30t) + 5, with t in hours. How many hours is one full cycle?

    Answerhours