Fall 1999, Math 100

CHAPTER 4
beginning with a preview of Chapter 7

Be sure to check back often, because assignments may change!

Due Monday 11/1 at 9am

Section 7.1: Introduction to the Trigonometric Functions

• 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 sin2(x); the Pythagorean identity.

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

1. 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)
2. What is sin(0o)? cos(0o)?
3. What is sin(90o)? cos(90o)?
4. What is sin2(27o) + cos2(27o)?

Reminders:

• 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 ...

Due Wednesday 11/3 at 9am

Section 7.1: Introduction to the Trigonometric Functions

• To read:middle of p. 430 - end
• Be sure to understand: What a radian is.

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

1. Why do we need radian measure?
2. Convert 120o to radian measure.
3. Convert 1 radian to degrees.

Reminders:

• Wednesday is the deadline for getting 100% on Gateway 3
• You have a quiz Thursday on Chapter 2.

Due Friday 11/5 at 9am

Section 7.4: Solving Trigonometric Equations: The Inverse Functions

• To read: middle of p. 465-end
• Be sure to understand: the restriction of domain for arcsine and arccosine.

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

1. For arcsin(x), why do we restrict the domain of sin(x)? What's special about the interval [-Pi/2,Pi/2)?
2. Without using a calculator, find arcsin(Pi/2).

Reminders:

• Bring questions on PS 8 to class on Friday

Due Monday 11/8 at 9am

Section 4.1: Polynomial Functions

• 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.

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

1. 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?
2. Construct a quadratic polynomial with real roots of x=2 and x=4.

Reminders:

• PS 8 is due Monday
• Midterm 2 is 11/18

Due Wednesday 11/10 at 9am

Section 4.1: Polynomial Functions

• 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.

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

1. How many turning points does a cubic polynomial have? How about inflection points?
2. Construct a cubic polynomial with roots x=-1, x=2, and x=4.
3. Can a cubic polynomial have 2 real roots and 1 imaginary root?

Reminders:

• 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!

Due Friday 11/12 at 9am

Section 4.4: Building New Functions From Old

• 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.

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

1. If f(x)=3x-4 and g(x)=1/x, find
1. (f+g)(3)
2. (f/g)(3)
2. Consider
R(x)=(3x3+5)/(x3-x2+x-1)

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

Reminders:

• Begin re-doing old problems, to study for Midterm 2.
• Bring questions on PS 9 to class Friday.

Due Monday 11/15 at 9am

Section 4.4: Building New Funtions from Old

• 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.

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

Let f(x)=x3+3x2 and g(x)=10x.
1. Find f o g(x)
2. Find g o f(x)

Reminders:

• PS 9 is due by 4pm Monday
• Re-do as many problems as you can, and do new ones too!

Due Wednesday 11/17 at 9am

Section 4.4: Building New Funtions from Old

• Be sure to understand: Composition, shifts, and stretching

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

1. Create a new function h(x) whose graph is identical to that of f(x), but shifted up by 4 units.
2. Create a new function j(x) whose graph is identical to that of g(x), but shifted right 4 units.

Reminders:

• 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.

Due Friday 11/19 at 9am

Section 4.6: Finding Polynomial Patterns

• 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.

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

1. Construct an interpolating polynomial of degree 2 that goes through the points P(0,6), Q(1,0), and R(2,-2).

Reminders:

• Bring questions on PS 10 to class on Friday

Due Monday 11/22 at 9am

Sections 4.4 and 4.6

• Be sure to understand: everything

1. None today

Reminders:

• PS 10 is due by 4pm Monday

And on to trigonometry we go! Next stop, Chapter 7!

Janice Sklensky
Wheaton College
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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