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Cogito

AP Precalculus · Chapter 6 · Lesson 2

Practice Worksheet

Sinusoidal Functions

Amplitude, period, midline and phase.

12 problems · about 22 minutes · AP Precalculus 3.5, 3.6, 3.7

NameDate

Figure — use these to answer the problems

Change b and count the cycles. Change c and the whole wave slides sideways.
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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 midline value?

    Answer

  2. Why factor the inside before reading a phase shift?

    • The shift is c after factoring, not the constant as written.
    • It is only a tidier way to write it.

  3. y = 7 sin x. What is the amplitude?

    Answer

  4. y = sin x + 4. What is the midline value?

    Answer

  5. y = sin(2x) in degrees. What is the period?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

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

    Answer

  2. y = 3 sin x + 5. What is the maximum value?

    Answer

  3. Max 20 and min 4. What is the amplitude?

    Answer

Stretch Yourself

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

4 problems

  1. Match each parameter with the feature it controls.

    Draw a line from each item on the left to its match on the right.

    • a
    • b
    • d
    • Amplitude
    • Period
    • Midline

  2. y = 2 sin x − 1. What is the minimum value?

    Answer

  3. The Amplitude

    Max 42 and min 2. What is the amplitude?

    Answer

  4. The Midline

    Same values. What is the midline?

    Answer