PreCalculus: 01/25/2007

Quickstart
Unit Circle Retake

(4.5) Graphs of Sine and Cosine Curves [continued]
Objective: Students will know how to sketch graphs of sine and cosine functions.

III. Translations of Sine and Cosine Curves
Vertical Translations - Graphing Calculator
What happens when d changes?
Graph
y = sin x
y = sin x + 1
y = sin x - 1
y = sin x - (1/2)
y = sin x + π
How does the graph change?

Vertical Translations - Sketching
Changing d changes the y-coordinates of our 5 critical points.
The five critical points will start with a y-coordinate of d if we are graphing the sine function and d + a if we are graphing a cosine function.

Use the Notetaking Guide to take notes

Homework
p. 331 #51, 53

PreCalculus: 01/24/2007

Quickstart
p. 330 #15 - 20 How do changes in equations change the graphs?
#98 - 101 Review converting radians to degrees

(4.5) Graphs of Sine and Cosine Curves [continued]
Objective: Students will know how to sketch graphs of sine and cosine functions.

III. Translations of Sine and Cosine Curves
Horizontal Translation - Sketching - 5 key points
Phase-shift = c / b
Period Interval: [c/b, c/b + 2π/b]

Practice p.330 #46

Homework
p.331 #45 - 53 odd

PreCalculus: 01/23/2007

Quickstart
p.330 #1 - 13 odd
Identify amplitude and period of sine and cosine curves from graph or equation.

(4.5) Graphs of Sine and Cosine Curves [continued]
Objective: Students will know how to sketch graphs of sine and cosine functions.

II. Amplitude and Period of Sine and Cosine Curves
Practice p.330 #30

III. Translations of Sine and Cosine Curves
Horizontal Translation - graphing calculator
What happens when we change c?
Graph on a graphing calculator
y = sin x
y = sin (x - π/4)
y = sin (x - π/2)
y = sin (x - π)
y = sin (x - 3π/2)
y = sin (x - 2π)
What happens to the graph?
Use the Student Success Organizer to take notes

Homework
p.331 #39, 41, 43

PreCalculus: 01/22/2007

Quickstart
p.321 #103
Average Temperature


(4.5) Graphs of Sine and Cosine Curves
Objective: Students will know how to sketch graphs of sine and cosine functions.
I. Basic Sine and Cosine Curves
y = sin x
Five Key Points
Intercept (0, 0)
Max (π/2, 1)
Intercept (π, 0)
Min (3π/2, -1)
Intercept (2π, 0)

y = cos x
Five Key Points
Max (0, 1)
Int (π/2, 0)
Min (π, -1)
Int (3π/2, 0)
Max (2π, 1)

General Form of Sine and Cosine equations
y = d + a sin (bx - c)
y = d + a cos (bx - c)

II. Amplitude and Period of Sine and Cosine Curves
What happens when we change a?
Use this website, Online Graphing Calculator,
to graph the functions below. See how the graph changes from y = sin(x)
y = 2sin x
y = 4sin x
y = (1/2)sin x
y = -sin x
y = (-1/2) sin x

Use the Student Success Organizer to take notes.

What happens when we change b?
Use the Online Graphing Calculator
to graph the functions below. See how the graph changes from y = sin(x)
y = sin(2x)
y = sin(4x)
y = sin((1/2)x)
y = sin(-x)

Use the Student Success Organizer to take notes.

Watch Video Tutor about Sine Functions
Watch Video Tutor about Cosine Functions