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Cogito

Integrated Math 3 · Chapter 5 · Lesson 2

Practice Worksheet

Graphing Sinusoidal Functions

Amplitude, period, midline and shift.

12 problems · about 21 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 the whole wave slides sideways.
-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. y = cos(3x) in degrees. What is the period?

    Answer

  2. Can an amplitude be negative?

    • No. It is a size, and a negative coefficient flips the wave instead.
    • Yes, when the coefficient is negative.

  3. y = 7 sin x. Amplitude?

    Answer

  4. y = sin x + 4. Midline value?

    Answer

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

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. y = 3 sin x + 5. Maximum value?

    Answer

  2. y = 2 sin x − 1. Minimum value?

    Answer

  3. y = −4 sin x. What is the amplitude?

    Answer

Stretch Yourself

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

4 problems

  1. Sort each change by the direction it acts in.

    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(6x) in degrees. Period?

    Answer

  3. The Period

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

    Answerdegrees

  4. The Shift

    y = sin(2x − 90°). What is the phase shift, in degrees?

    Answerdegrees