Class meeting 
Topic 
Assignment 
Tuesday, Jan.
14 
Section 7.1
Periodic Functions 
Welcome to our class.
Handouts: Ferris Wheel (See pictures of the London Eye:
1
2
3)
Syllabus
Internet Resources (with a link to the
General Course Information)
Today's objectives:
1. Identify if a graph represents a periodic function.
2. Determine period, amplitude and midline.
3. Use a graph to find and interpret y if given t or vice
versa.
Due: Thursday, January 16
Read:
General Course Information, the Syllabus, and, if you have the
text, Section
7.1 and
7.2
Do: If necessary, purchase a TI84 Plus
CE or equivalent and purchase eHW access.
Note: access is
good for one year.
Practice on eHW
Flash Cards: 7.1 Periodic Functions.
Optional: Section 7.1  your choice of 117, 2334 as
needed.
Review
eHW Math
Background Needed for MA 15400 and
eHW
Flash Cards for Prerequisite Skills
See also
Practice Questions to Check Prerequisite Skills Needed for MA 15400
and these
Worked out Solutions.
You should also
be proficient in these
skills needed for MA 15300.
Prepare for QUIZ 1 next Tuesday, Jan. 21 over
prerequisite skills.
Due
Friday, January 17, 11:59 pm:
EHW: Quiz on John's Syllabus Score 90% or Higher by the Deadline!
Note: You need to get a score of 90% or higher for this eHW by the
deadline to open up any future eHW assignments.
You have unlimited attempts.
Due Monday, Jan. 20, 11:59 pm:
EHW0: General Course
Information and Using eHW
Due Monday, Jan. 20, 11:59 pm:
EHW: Math Background Needed for MA 15400
Due Thursday, Jan. 23, 11:59 pm:
EHW 01
Sections 7.1  7.2 
Thursday, Jan.
16 
Section 7.2
The Sine Function
(and its Sidekick, Cosine) 
Today's objectives:
 Sketch the position of a point on a circle of radius r
corresponding to a given angle (or value of time or number
of revolutions) and give its coordinates
 Find angles between 0° and 360° which have the same sine or cosine of a given angle.
 Determine in which quadrant an angle lies if given
certain conditions.
Do (for practice): Flash
Card
7.2 Report the coordinates of a point on a circle of radius r given
the angle. Flash Card
7.2 Use the definitions of sine and cosine
Flash Card
7.2 Find angles which have the same sine (or cosine) as a given
angle
If you have a text, read Section
7.3
and do Section 7.2 
1, 3, 531 
Click on the photo to enlarge (and download for
printing).

Prepare for QUIZ 1 next Tuesday, Jan. 21 over
prerequisite skills.
(For practice do
eHW Math
Background Needed for MA 15400 and review
eHW
Flash Cards for Prerequisite Skills
See also
Practice Questions to Check Prerequisite Skills Needed for MA 15400
and the
Worked out Solutions.)
Due
Friday, January 17, 11:59 pm:
EHW: Quiz on John's Syllabus Score 90% or Higher by the Deadline!
Note: You need to get a score of 90% or higher for this eHW by the
deadline to open up any future eHW assignments.
You have unlimited attempts.
Due Monday, Jan. 20, 11:59 pm:
EHW0: General Course
Information and Using eHW
Due Monday, Jan. 20, 11:59 pm:
EHW: Math Background Needed for MA 15400
Due Thursday, Jan. 23, 11:59 pm:
EHW 01
Sections 7.1  7.2 

Class meeting 
Topic 
Assignment 
Tuesday, Jan.
21 
Section 7.3
Radians 
Today's objectives:
 Convert an angle from degrees to radians and vice versa.
 Interpret the radian measure of the central angle of a
circle of radius r as the number of radius lengths, r,
that you need to wrap around the rim of the circle on the arc
spanned by the angle.
 Understand the relationship between arc length, radius and
an angle measure in radians.
If given two of the arc length s, radius r, or an
angle θ, find the third.
The radian measure of an angle θ is the number of radius
lengths that a bug would walk on the rim of a circle spanned by the
angle.
For a circle of radius r, if s is the arc length
the bug walks on the rim, then we have
s = (the radius r)
x (# of radius lengths) or
s = r
x θ
Here is a short video
of the bug taking a tour around the rim of a circle,
counting radius lengths as he goes. It is a silent movie since bugs can't talk. 

Suppose a central angle θ in a circle
of radius r spans an arc of length s. Measure how
many radius lengths that the length of the arc is. This number of
radius lengths is the radian measure of the angle θ: we
have rθ = s.


Do (for practice):
Flash Card 7.3 Degrees <=> Radians
Flash Card 7.3 Find points on a circle using radian
measure of quadrantals
Flash Card 7.3 Radian Measure as Number of Radius Lengths Around
a Circle
Flash Card 7.3
Arc Length of a Sector
If you have a text, read
Chapter 7 Skills Refresher,
see Section 7.3  156 as desired (for practice).
Due Thursday, Jan. 23, 11:59 pm:
EHW 01
Sections 7.1  7.2
Due Tuesday, Jan. 28, 11:59 pm:
EHW 02
Section 7.3
Due
Thursday, Jan. 30 
Writing Assignment 1: Bug on a Square Track
For next class, Thursday, Jan. 23, please come prepared with the
first two pages of WR1 completed.

Thursday, Jan.
23 
Today: Special Angles 
Handout: Unit circle with exact values
We worked some problems from Writing Assignment 2 on finding angles in
radians (exactly).
Today's objectives:
1. Find exact values of sine and cosine for multiples of 30°, 45°, and 60° or their radian equivalents π/6, π /4, or π /3.
2. Use proportional reasoning to find sides of special triangles.
3. Solve simple trig equations over a requested interval; for example on the
interval [0, 2π) find θ if sin θ = 1/2, providing exact values
of angles measured in radians when they are multiples of π/6, π /4, or π /3.
Be aware of when more than one solution exists! Be able to sketch the angle
or angles.
Due: Tuesday, Jan. 28
Do (for practice):
Flash Card Chapter 7 Skills Refresher Properties of Special Triangles
Flash Card Chapter 7 Skills Refresher Exact Values of Sine and Cosine
If you have a text, see
Chapter 7
Skills Refresher
(page 324)  1 31 as desired (for practice).
Due tonight, Thursday, Jan. 23, 11:59 pm:
EHW 01
Sections 7.1  7.2
Due Tuesday, Jan. 28, 11:59 pm:
EHW 02
Section 7.3
Due
Thursday, Jan. 30, 11:59 pm:
EHW 03
Chapter 7 Skills Refresher
Due
Thursday, Jan. 30 
Writing Assignment 1: Bug on a Square Track
Due Tuesday, Feb. 4  Writing Assignment 2: What's My Angle?
For Tuesday, Jan. 28: QUIZ 2 over 7.1 and 7.2 

Class meeting 
Topic 
Assignment 
Tuesday, Jan.
28 
Section 7.4 Graphs of
Sine and Cosine 
Today's objectives:
1. Know the main characteristics (period, amplitude, midline, domain, range,
odd/even symmetry, when it is positive, negative, increasing, decreasing, if
it starts at or above the midline) of the graph of y = sin θ,
and y = cos θ. Relate this to the unit circle as the xcoordinate
(cosine) or the ycoordinate (sine) of the point on the circle.
2. For y = Asin(x) + k or y = Acos(x)
+ k , identify the period, amplitude, and midline.
We discussed the domain, range, period, and amplitude of y
= sin(x) and y = cos(x) and how these can be
determined from the unit circle.
We looked at an outside change to the
function, which results in the original function being transformed vertically
(change to the output).

y = Asin(x) and y = Acos(x)
have amplitude A.
For A > 0,
the graph of y = Asin(x) vertically stretches or
compresses the graph of y = sin(x) by A units.
the graph of y =
–Asin(x)
is a vertical reflection of the graph of y = Asin(x).
Similarly for y = cos(x).

y = sin(x) + k and y = cos(x)
+ k have midline k.
For k > 0,
the graph of y = sin(x) + k vertically shifts
the graph of y = sin(x) up k units.
the graph of y = sin(x)
– k
vertically shifts the graph of y = sin(x) down k
units.
Similarly for y = cos(x).
The first multiplies the output by a quantity; the second
adds/subtracts a quantity to the output.
For the function y = Asinx + k
or y = Acosx + k
we explored the effects of A and k to find that
this graph has
an amplitude of A, and midline which is y = k.
Due: Thursday, Jan. 30
Optional:
Section 7.4 
124,
2630, 3438 and Chapter 7 Review 14a, 14d, 1924, 51, 52, 6971
and read Section 7.5
Practice on eHW Flash Cards: 7.4 Period, Amplitude, Midline
Due tonight, Tuesday, Jan. 28, 11:59 pm:
EHW 02
Section 7.3
Due
Thursday, Jan. 30, 11:59 pm:
EHW 03
Chapter 7 Skills Refresher
Due
Thursday, Jan. 30 
Writing Assignment 1: Bug on a Square Track
Due Tuesday, Feb. 4  Writing Assignment 2: What's My Angle? 
Thursday, Jan.
30 
Section 7.5
The graph of
y = sin(Bx)
(Inside
multiplicative change) 
For the function y = AsinBx + k
or y = AcosBx + k
we explored the effects of B on the period to find that,
for positive values of B, this graph has
a period of 2π/B.
Today's objectives:
1. Report the period of the graph of y = AsinBx +
k.
2. If you have found the period, p, of y = sinBx,
check that your value is correct by substituting into the formula and
verifying that B·p
= 2π.
3. Given a graph, report the midline, amplitude and period and use them
to find the formula y = AsinBx + k
or y = AcosBx + k.
Do (for practice):
Flash Card 7.4
Period, Amplitude, Midline
Flash Card 7.5
Find a Formula of a Sine or Cosine Function (No Phase Shift Needed)
Flash Card 7.5
Find a Formula of a Sine or Cosine Function (Ferris Wheel)  then find y
if given x
Flash Card 7.5
Find a Formula of a Sine or Cosine Function (Ferris Wheel)  then find x
if given y
If you have a text, see
Section 7.5  112, 2126 and read Section
7.5 and, if needed, Sections 2.4, 6.1, 6.2
Due
tonight, Thursday, Jan. 30, 11:59 pm:
EHW 03
Chapter 7 Skills Refresher
Tuesday, Feb. 4: QUIZ
3 over Section
7.3
and Chapter 7 Skills Refresher
Due Tuesday,
Feb. 4 
Writing Assignment 2: What's My Angle?
Due Tuesday,
Feb. 11 
Writing Assignment 3: Trig Graphs 

Class meeting 
Topic 
Assignment 
Tuesday,
Feb. 4 
Section 7.5
For positive values of
A, B, h, k, and φ
we explored the graph of
y = Asin(B(x − h)) + k or y = Asin(Bx − φ) + k
where h is the
horizontal shift to the right and
where φ = Bh is the
phase shift to the right 
Today: QUIZ 3 over
7.3 and Chapter 7 Skills Refresher
Continued Section 7.5. If given a graph, find the midline,
period, amplitude, and the horizontal and phase shifts. When specifying
horizontal and phase shift, include whether it is regular sine or cosine
(or upside down versions of these), whether it is shifted left or right,
and by how much.
Today's objectives:
1. Given a graph and a model choice (regular or upside down sine or
cosine) report the phase shift.
2. Given a graph with a nonzero phase shift φ or horizontal shift h, find
a formula y = Asin(B(x−h))+ k or y =
Asin(Bx−φ) + k.
3. If you have found the phase shift, φ, of the graph of
y =sin(Bx−φ), check that your value is correct by multiplying out y =sin(B(x−h))
and verifying that B·h
= φ, where h is the horizontal shift.
Do (for practice)::
Flash Card 7.5
Find Phase Shift
Flash Card 7.5
Find a Formula of a Sine or Cosine Function (Phase Shift Needed)
Optional:
Section 7.5  2731, 37, 38, 4450 and read Section 7.6 and,
if needed, Sections 2.4, 6.1, 6.2
Due Tuesday,
Feb. 11 
Writing Assignment 3: Trig Graphs
Due Tuesday, Feb. 11, 11:59 pm:
EHW 04 Section 7.47.5 



