Cogito
Trigonometry · Chapter 3 · Lesson 1
Amplitude, Period, and Shift
Reading a wave from its equation.
10 problems · about 21 minutes · F-TF.B.5, F-IF.C.7
What this lesson teaches
The student graphs sine and cosine functions and identifies amplitude, period, phase shift, and midline.
- Amplitude is the height above the midline.
- The period is 2π divided by the coefficient of x.
- An added constant sets the midline.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Arc Length and Angular Speed: Radius 7, angle 2 radians. What is the arc length?
Answer 14
Why 14.
Review — Reference Angles and the Four Quadrants: What is the reference angle for 200°, in degrees?
Answer 20
Why 20°.
Warm Up
Straightforward practice. Get the method working first.
4 problemsy = 6 sin x + 2. Maximum value?
Answer 8
Why 8.
What does the coefficient of x inside sine control?
Answer The period.
Why It sets the period.
y = 4 sin x. Amplitude?
Answer 4
Why The front multiplier.
y = sin x + 6. Midline?
Answer 6
Why The added constant.
Build It Up
The same ideas with more to keep track of.
2 problemsy = 3 sin x − 2. Minimum value?
Answer -5
Why Midline minus amplitude.
y = sin(4x). Period is 2π divided by what?
Answer 4
Why The coefficient of x.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Amplitude: y = 5 sin x. What is the amplitude?
Answer 5
Why 5.
The Maximum: y = 2 sin x + 3. What is the maximum value?
Answer 5
Why 5.