Week 11 of m151
(§ 2, Mr. Lane)
10–14 April 2017

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

math@Mansfield (Library) has tutors: 6:30pm – 9:00pm on Sunday–Thursday

- Monday [d34] (10 April 2017)
WeBWorK:
RQ-9-1 closes at 10 am,
day-32 closes at 11 pm
- Study section 9.1 (
*Trigonometric Equations*).- A graph of f(x) together with line y = C on interval [a,b] can help count number of solutions for f(x) = C. Zoomed views can help find approximate solutions.
- If f(x) involves a Sine or Cosine or Tangent function, then an inverse-trig function may find one solution of f(x) = C. More solutions can be found using periodicity or other geometry.
- Solving inequality f(x) ≤ C can use graphs of f(x) and C to clarify nature of the solution set; follow that with use of equation-solving techniques to locate end-points of solution set for the inequality.

- Work on these problems in section 9.1:
**2**, 9, 11; 15, 23, 31,**35**, 41

- Study section 9.1 (
- Tuesday [d35]
WeBWorK:
RQ-9-2 closes at 10 am,
day-33 closes at 11 pm
- Study section 9.2 (
*Identities, Expressions, and Equations*)- Examples 1–5 use Identities from Chapter 7 for several tasks: Simplify, Evaluate, Solve.
- The
*Double-Angle Formula for Sine*(page 361 & Example 6) introduces a new tool. - There are three
*Double-Angle Formulas for Cosine*.

- Work on these problems in section 9.2:
1, 3,
**7**, 9, 15, 17,**26**; 30, 35,**55**, 59, 61, 66 - Anticipate a quiz on Tuesday or Wednesday.

- Study section 9.2 (
- Wednesday [d36]
WeBWorK:
RQ-9-3 closes at 10 am,
day-34 closes Thursday at 11 pm
- Study section 9.3
(
*Sum and Difference Formulas for Sine and Cosine*). - Work on these problems in section 9.3:
**9**, 11, 12; 17, 18,**23**, 27 - Problems 23–25 compute average rates of change on the interval between x and x+h for the periodic functions Cosine, Sine, Tangent. A calculus class will show why their results are important.

- Study section 9.3
(
- Friday [d37]
WeBWorK:
RQ-9-4 closes at 10 am,
day-35 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**8.3 9.1 9.2 9.3 **problems**50 40 56 28 - We will not study the first half of section 9.4: skip Examples 1—6.
- Study last half of section 9.4: begin at bottom of page 374 with
*Sums and Differences of Sines and Cosines:*.**Same Periods**- The discussion on page 376 uses the Sine-Addition formula which is the first of the boxed formulas on page 365.
- The boxed summary on page 377 shows how to determine Amplitude and Phase Shift for a sum of two sinusoidal functions with the same period.
- Computing A and φ given a
_{1}and a_{2}is strongly related to finding polar coordinates for a point after being given its rectangular coordinates. (Study the two sentences below the boxed summary on page 377.) - Try to solve Example 9 on your own (or with minimal use of the text's discussion).

- Work on these problems in section 9.4:
3 (modify Example 7, then check your work [graphically]),
4 (see Example 8), 1 & 2;
**15** - Section 9.5 is not on the syllabus for this course (and its topics will not be on an exam). However, I recommend a casual reading of the bottom half of page 381 and examination of three graphs which show interesting behavior that is a simplified version of acoustic phenomena.

- Write-up solutions of these four problems —
show your work and interpret your results. Hand-in your written
homework at the

© Richard B Lane
Last modified: 7 April 2017, Friday 06:57