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

Reading questions:

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

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

Reading questions:

1. Why do we need radian measure?
2. Convert 120^o 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

Reading questions:

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

Reading questions:

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

Reading questions:

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

Reading questions:

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

Reading questions:

Let f(x)=x³+3x² and g(x)=10^x.
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

• To read: Re-read Section 4.4
• Be sure to understand: Composition, shifts, and stretching

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

Reading questions:

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

Reading questions:

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

• To read:re-read Sections 4.4 and 4.6
  
• Be sure to understand: everything
  

Reading questions:

1. None today

Reminders:

• PS 10 is due by 4pm Monday