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Cogito

Trigonometry · Chapter 3 · Lesson 1

Practice Worksheet

Amplitude, Period, and Shift

Reading a wave from its equation.

10 problems · about 21 minutes · F-TF.B.5, F-IF.C.7

NameDate

Figure — use these to answer the problems

Change the amplitude and the frequency separately, and name what moved.
-8-8-6-6-4-4-2-222446688
y = 2 sin(1x) + 0
  • Point(1, 1.68)
Amplitude a2
Frequency b1
Midline0
Read at x1
Figure 1

Warm-Up Review

From earlier lessons. Loosen up before the new work.

2 problems

  1. From “Arc Length and Angular Speed”

    Radius 7, angle 2 radians. What is the arc length?

    Answer

  2. From “Reference Angles and the Four Quadrants”

    What is the reference angle for 200°, in degrees?

    Answer

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. y = 6 sin x + 2. Maximum value?

    Answer

  2. What does the coefficient of x inside sine control?

    • The period.
    • The amplitude.

  3. y = 4 sin x. Amplitude?

    Answer

  4. y = sin x + 6. Midline?

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

  1. y = 3 sin x − 2. Minimum value?

    Answer

  2. y = sin(4x). Period is 2π divided by what?

    Answer

Stretch Yourself

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

2 problems

  1. The Amplitude

    y = 5 sin x. What is the amplitude?

    Answer

  2. The Maximum

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

    Answer