Cogito
Integrated Math 3 · Chapter 5 · Lesson 2
Graphing Sinusoidal Functions
Amplitude, period, midline and shift.
12 problems · about 21 minutes · F-TF.B.5, F-IF.C.7
What this lesson teaches
The student determines the four features of a sinusoidal function from its equation.
- A sinusoid is a sin(b(x − c)) + d, with one feature per letter.
- The period is 360 ÷ b, and horizontal changes behave backwards.
- Factor the inside before reading the phase shift.
Warm Up
Straightforward practice. Get the method working first.
5 problemsy = cos(3x) in degrees. What is the period?
Answer 120
Why 120°.
Can an amplitude be negative?
Answer No. It is a size, and a negative coefficient flips the wave instead.
Why Amplitude is the size of the coefficient.
y = 7 sin x. Amplitude?
Answer 7
Why The coefficient.
y = sin x + 4. Midline value?
Answer 4
Why The constant.
y = sin(2x) in degrees. Period?
Answer 180
Why 360 ÷ 2.
Build It Up
The same ideas with more to keep track of.
3 problemsy = 3 sin x + 5. Maximum value?
Answer 8
Why Midline plus amplitude.
y = 2 sin x − 1. Minimum value?
Answer -3
Why Midline minus amplitude.
y = −4 sin x. What is the amplitude?
Answer 4
Why Amplitude is a size.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsSort each change by the direction it acts in.
Answer Horizontal: The b in sin(bx), The c in sin(x − c) · Vertical: The a in a sin x, The d in sin x + d
Why Inside the function is horizontal; outside is vertical.
y = sin(6x) in degrees. Period?
Answer 60
Why 360 ÷ 6.
The Period: y = sin(4x) in degrees. What is the period?
Answer 90 degrees
Why 90°.
The Shift: y = sin(2x − 90°). What is the phase shift, in degrees?
Answer 45 degrees
Why 45°.