**To read:**pp. 425-middle of p. 430**Be sure to understand:**what a unit circle is and how it used to develop the graphs of sin(theta) and cos(theta); the relationship between the triangle definitions and the circular definitions of the trig functions; the meaning of the notation sin^{2}(x); the Pythagorean identity.- Consider a 3-4-5 right triangle (where 5 is, of course, the length of the hypotenuse. Let x be the angle opposite the side of length 3. Find
- sin(x)
- cos(x)

- What is sin(0
^{o})? cos(0^{o})? - What is sin(90
^{o})? cos(90^{o})? - What is sin
^{2}(27^{o}) + cos^{2}(27^{o})? - PS 7 is due by 4pm Monday.
- Wednesday is the deadline for getting full credit on gateway 3.
- There's a quiz on Thursday 11/4, which will cover chapter 2. While it is just a quiz, rather than a gateway (as that seemed to be what you wanted), you should study some for it, as you don't get to take it over and over again ...
**To read:**middle of p. 430 - end**Be sure to understand:**What a radian is.- Why do we need radian measure?
- Convert 120
^{o}to radian measure. - Convert 1 radian to degrees.
- Wednesday is the deadline for getting 100% on Gateway 3
- You have a quiz Thursday on Chapter 2.
**To read:**middle of p. 465-end**Be sure to understand:**the restriction of domain for arcsine and arccosine.- For arcsin(x), why do we restrict the domain of sin(x)? What's special about the interval [-Pi/2,Pi/2)?
- Without using a calculator, find arcsin(Pi/2).
- Bring questions on PS 8 to class on Friday
**To read:**p. 179 - middle of p. 184**Be sure to understand:**How the behavior of polynomials can differ from the other families of functions we've studied. What the degree of a polynomial is. The connections between power functions, linear functions, and polynomials. The difference between a function and an equation; the difference between zeros and roots. The connection between real roots, x-intercepts, and linear factors. Know how to use the quadratic formula, of course.- For each family of functions we've discussed so far, how many turning points can such a function have? How many inflection points? What can polynomials do that the others can not?
- Construct a quadratic polynomial with real roots of x=2 and x=4.
- PS 8 is due Monday
- Midterm 2 is 11/18
**To read:**middle of p. 184 - end**Be sure to understand:**How many roots an nth degree polynomial can have; how many**real**roots an nth degree polynomial can have; the connection between real roots, x-intercepts, and linear factors; how to find a polynomial if you're given its roots, degree and y-intercept; the connection between a repeated root and the behavior of the graph at that point discussed on page 187.- How many turning points does a cubic polynomial have? How about inflection points?
- Construct a cubic polynomial with roots x=-1, x=2, and x=4.
- Can a cubic polynomial have 2 real roots and 1 imaginary root?
- Midterm 2 is 11/18. It will cover through Section 4.1. Make sure you've done every single problem that I've assigned.
- We are beginning Project 2 on the Monday before Thanksgiving, so it is crucial that you come to class that day! Vacation does not begin until after classes are over on Tuesday!
**To read:**pp 208 - middle of p. 213**Be sure to understand:**how you get the graph of (f+g)(x) from the graphs of f(x) and g(x); how to analyze the behavior of (fg)(x) and (f/g)(x)--which terms dominate, any asymptotes, etc.

- If f(x)=3x-4 and g(x)=1/x, find

- (f+g)(3)
- (f/g)(3)

- Consider

R(x)=(3x ^{3}+5)/(x^{3}-x^{2}+x-1)

- Calculate R(100), R(1000), R(100,000).
- What would you guess happens to the graph of R(x) as x approaches infinity?

- Begin
**re-**doing old problems, to study for Midterm 2. - Bring questions on PS 9 to class Friday.
**To read:**p. 213 - end**Be sure to understand:**what a composition of functions is; vertical and horizontal shifts, stretching and compressing by multiplying by a constant.

- Find f o g(x)
- Find g o f(x)
- PS 9 is due by 4pm Monday
- Re-do as many problems as you can, and do new ones too!
**To read:**Re-read Section 4.4**Be sure to understand:**Composition, shifts, and stretching- Create a new function h(x) whose graph is identical to that of f(x), but shifted up by 4 units.
- Create a new function j(x) whose graph is identical to that of g(x), but shifted right 4 units.
- Midterm 2 is Thursday. If you haven't signed up for a time to take it, let me know.
- Make sure you work on the study guide.
**To read:**Section 4.6: pp 232-234;

skim 235-middle of p. 241

read middle of p. 241-p. 245

**Be sure to understand:**2nd and 3rd differences. If you have 6 distinct points (with different independent variables), what is the smallest degree polynomial that is guaranteed to contain them? Example 4.

- Construct an interpolating polynomial of degree 2 that goes through the points P(0,6), Q(1,0), and R(2,-2).
- Bring questions on PS 10 to class on Friday
**To read:**re-read Sections 4.4 and 4.6

**Be sure to understand:**everything

- None today
- PS 10 is due by 4pm Monday

Fall 1999, Math 100

**CHAPTER 4**

beginning with a preview of Chapter 7

** Due Monday 11/1 at 9am**

**Section 7.1: Introduction to the Trigonometric Functions**

**E-mail Subject Line:** Math 100 Your Name 11/1

**Reading questions:**

**Reminders:**

** Due Wednesday 11/3 at 9am**

**Section 7.1: Introduction to the Trigonometric Functions**

**E-mail Subject Line:** Math 100 Your Name 11/3

**Reading questions:**

**Reminders:**

** Due Friday 11/5 at 9am**

**Section 7.4: Solving Trigonometric Equations: The Inverse Functions**

**E-mail Subject Line:** Math 100 Your Name 11/5

**Reading questions:**

**Reminders:**

** Due Monday 11/8 at 9am**

**Section 4.1: Polynomial Functions**

**E-mail Subject Line:** Math 100 Your Name 11/8

**Reading questions:**

**Reminders:**

** Due Wednesday 11/10 at 9am**

**Section 4.1: Polynomial Functions**

**E-mail Subject Line:** Math 100 Your Name 11/10

**Reading questions:**

**Reminders:**

** Due Friday 11/12 at 9am**

**Section 4.4: Building New Functions From Old**

**E-mail Subject Line:** Math 100 Your Name 11/12

**Reading questions:**

**Reminders:**

** Due Monday 11/15 at 9am**

**Section 4.4: Building New Funtions from Old**

**E-mail Subject Line:** Math 100 Your Name 11/15

**Reading questions:**

- Let f(x)=x

**Reminders:**

** Due Wednesday 11/17 at 9am**

**Section 4.4: Building New Funtions from Old**

**E-mail Subject Line:** Math 100 Your Name 11/17

**Reading questions:**

**Reminders:**

** Due Friday 11/19 at 9am**

**Section 4.6: Finding Polynomial Patterns**

**E-mail Subject Line:** Math 100 Your Name 11/19

**Reading questions:**

**Reminders:**

** Due Monday 11/22 at 9am**

**Sections 4.4 and 4.6**

**Reading questions:**

**Reminders:**

Department of Mathematics and Computer Science

Science Center, Room 109

Norton, Massachusetts 02766-0930

TEL (508) 286-3973

FAX (508) 285-8278

jsklensk@wheatonma.edu

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