Week 8 of m151
(§ 2, Mr. Lane)
13–17 March 2017
In 2017,
Daylight Time begins Sunday, March 12 —
set your clock ahead one hour at 2 am.
Math Learning Center (in Math 011) has tutors:
9am–4pm on Monday–Thursday and 9am–1pm on Friday
math@Mansfield (Library) has tutors:
6:30pm – 9:00pm on Sunday–Thursday
- Course grade in m151 depends on four mid-term tests (400 points),
Final Exam (200), homework & quizzes (200).
- The first half-semester Homework+Quiz score
(percentage of about 350 points) had about
two-thirds of its points from WeBWorK assignments and the remaining
one-third from written homework and in-class quizzes.
- Although the effect of missing a few assignments is relatively small,
the overall effect of not doing most of the homework
is as severe as not completing work on a mid-term test.
- The Homework+Quiz score for the second half-semester will be percentage
of points for online and written work due after March 12.
- Monday (13 March 2017) [d24] —
first day of second half-semester:
see comments (above) about Homework+Quiz score
WeBWorK:
RQ-7-2 closes at 10 am,
day-22 closes at 11 pm
- Study section 7.2 (The Sine and Cosine Functions).
- The Unit Circle is centered at the origin
with radius 1.
- Angles in The Unit Circle generalize angles in a right triangle.
- Notice where Cosine has negative values.
Notice where Sine has negative values.
- Symmetry and Reference Angles: values of (Cos,Sin)
in first quadrant imply values in other quadrants.
- Work on these exercises and problems in section 7.2:
1, 2–4, 5, 9, 11, 19;
21, 23, 25, 27, 28, 35, 36
- Tuesday [d25]
WeBWorK:
RQ-7-3 closes at 10 am,
day-23 closes at 11 pm
- Study the Skills Refresher: Special Angles section at the
end of Chapter 7 (pages 322–325).
- Ideas in § T.3–T.4 for some special right triangles
are discussed in context of The Unit Circle together with
the Sine & Cosine functions.
- Examples 1 & 2 compute sine and cosine for some
special angles (see bottom of page 283).
- Study section 7.3 (Radians and Arc Length).
- A radian is an intrinsic measure for size of an angle
(and a corresponding circular arc with that angle).
- Radians are the conventional unit for input to
sin, cos, and tan.
Unless a use of those functions specifies input
is measured in degrees (or more esoteric units such as
grad or mil),
you should presume radians are to be used
in a text or WeBWorK problem.
- Work on these exercises and problems in section 7.3:
1, 7, 9, 14, 18, 21, 24;
25, 35, 39, 45, 47, 51, 52
- Anticipate a quiz on Tuesday or Wednesday.
- Wednesday [d26]
WeBWorK:
RQ-7-4 closes at 10 am,
day-24 closes at 11 pm
- Study section 7.4 (Graphs of the Sine and Cosine).
- Table 7.5 and Figure 7.45 (start of §7.4) show θ
in both degrees and radians; later figures use radians.
- Midline and Amplitude were introduced earlier
(p 269); identifying each remains important (p 287).
- Work on these exercises & problems in section 7.4:
1, 5, 7, 9, 11, 13, 15;
17, 18, 20, 26, 31, 35
- Study section 7.5 (Sinusoidal Functions) through Example 3.
- After reading definition of Periodic Function and the
Period of a periodic function, write a one-sentence
description of several contexts where an observable quantity
has a periodic behavior.
- Study Examples 1 & 2 carefully to understand how an
inside scale change modifies the period of a
function.
- Work on these exercises and problems in section 7.5:
5, 11, 15;
25, 27, 33
- Friday [d27]
WeBWorK:
RQ-7-5 closes at 10 am,
day-25 closes Saturday at 11 pm
- Write-up solutions of these four problems —
show your work and interpret your results. Hand-in your written
homework at the start of Friday's class.
section |
7.1 |
7.2 |
7.3 |
7.4 |
problems |
34 |
30 |
50 |
34 |
- Resume study of §7.5 on page 295 (Horizontal Shift).
Notice how h and k are used in the boxed summary on
page 296. Compare their effect in this context with their role in the
vertex form for a quadratic function (see page 124).
- Phase Shift (pages 297–298) lets a horizontal shift be described
as some fraction of a period.
The technical term Phase Shift (or phase angle) is
used in several types of science and engineering.
- Work on more exercises and problems in section 7.5:
3, 7, 13, 19;
37, 41, 45, 47, 50
© Richard B Lane
Last modified: 16 March 2017, Thursday 19:07