Fall 1997, Math 100
Chapter 7

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

### Section 7.1 Introduction to the Trigonometric Functions

• To read: All of the section. Also read Appendix A, if you've never seen right triangle trig.
• Remember: you need to pass the gateway before Thanksgiving to get the full 100%.
• Be sure to understand:Why the cosine and sine functions vary between -1 and 1, and what their graphs have to do with the unit circle.
1. Name four values of x for which cos(x)=0 (in degrees and radians).
2. What does the graph of
f(x)=cos2(x)+sin2(x)

look like?
What is f(pi/6)?
3. Convert 120 degrees to radians.
• E-mail subject line: Math 100 Your Name 11/14

### Section 7.2 Trigonometric Functions and Periodic Behavior

• To read: thru page 439
• Be sure to understand: how to shift a trigonometric graph vertically, and how to stretch and compress them.
1. Look at the graphs of 2sinx-4 and sinx on your graphing calculator. What is the effect of the 2? How about the -4?
2. Let f(x)=sinx and g(x)=sin(2x). Calculate the following, without using a calculator (you need to get comfortable with these values). The inputs are in degrees.
1. What are f(0) and g(0)?
2. What are f(30) and g(30)?
3. What are f(45) and g(45)?
4. f(x) goes through one cycle (or period) every 360 degrees. In other words, when x reaches 360 degrees, f(x) begins repeating itself. For what x will g(x) have gone through the entire cycle of values and begin repeating itself?
• E-mail subject line: Math 100 Your Name 11/17

### Section 7.2 Trigonometric Functions and Periodic Behavior

• Be sure to understand: The frequency and phase shift
1. Let f(x)=sinx and g(x)=sin(4x). Calculate the following, without using a calculator. The inputs are in radians.
1. What are f(0) and g(0)?
2. What are f(pi/4) and g(pi/4)?
3. What are f(pi/3) and g(pi/3)?
4. What are f(pi/2) and g(pi/2)?
5. How many cycles does g(x) complete between 0 and 2pi?
• E-mail subject line: Math 100 Your Name 11/19

### Section 7.3 Relationships Between Trigonometric Functions

• To read: All of it
• Be sure to understand: the Pythagorean and the reflection identities
1. Use trig identities to write cos(-2x) in terms of sinx and cosx.
2. Use trig identities toowrite sin(4x) in terms of sinx and cosx. (Hint: first write sin(4x) in terms of sin(2x) and cos(2x).)
• E-mail subject line: Math 100 Your Name 11/21

### 11/24

Happy Thanksgiving!!

### Section 7.4: Solving Trig Equations: The Inverse Function

• Be sure to understand: How to find Arcsin(x) by looking at a graph of Sin(x). Why you cannot take the Arcsine of numbers bigger than 1 or less than -1.
1. When defining Arcsin(x), why do we focus our attention on the portion of the graph of Sin(x) that is between -pi/2 and pi/2?
2. Without using your calculator (using only your circle), find Arcsin(1/2) and Arcsin(4).
Also be sure to pass the gateway, if you haven't already! (If you haven't passed it yet, you've missed your chance to get 100% on it, but you can still get 90% on it through next Monday, December 8.)
• E-mail subject line: Math 100 Your Name 12/1

### Section 7.5: The Tangent Function

• Be sure to understand:How the tangent function is related to the sine and cosine functions. Why tan2x+1=1/cos2x.
1. Without using your calculator, but using your circle and the definition of tangent, find tan(0), tan (pi/6), tan(pi/4), tan(pi/3), and tan(pi/2).
• Also be sure to: begin studying for the exam on Monday! See the assignment for 12/5 for some suggestions on studying.
• E-mail subject line: Math 100 Your Name 12/3

### Study for Exam!

• To read: Sections 2.6 and 2.7, Chapter 4, Chapter 7
• Be sure to understand: Everything
• Study Suggestions:
1. Do not put off studying for this exam until the day before. Begin at least the wednesday before!
3. Read the chapter summaries at the end of both chapters.
4. Make lists of the main points of each section. Think about why we care about each of those topics and how they're all related.
5. Do the problems on the study guide.
6. Do the review problems at the end of each chapter.
7. Look over all your homework, and redo as many of them as you have time for.
8. Come look at, or better yet photocopy, my solutions to the homework problems. Use them as yet another study guide.
9. Look for the big picture, and for patterns. How are the various topics similar? How are they different? Were there some ideas that showed up over and over again? Did we do the same process repeatedly?

### 12/10

I am either going to make your final available today or Friday the 12th. I will put it in a sealed envelope for you. You may pick it up anytime after it's available, but you may not look in the book or at your notes after you open the envelope. It will be due at 11am on Wednesday the 17th.

### Study for Final

• Be sure to understand: everything
• Study Suggestions:
1. Do not put off studying for this exam until the day before.
3. Read the chapter summaries at the end of both chapters.
4. Make lists of the main points of each section. Think about why we care about each of those topics and how they're all related.
5. Do the problems on the study guide.
6. Do the review problems at the end of each chapter.
7. Look over all your homework, and redo as many of them as you have time for.
8. Come look at, or better yet photocopy, my solutions to the homework problems. Use them as yet another study guide.
9. Look for the big picture, and for patterns. How are the various topics similar? How are they different? Were there some ideas that showed up over and over again? Did we do the same process repeatedly?

Here Endeth the Semester!

Good Luck on the Final!

Have a Wonderful Winter Break!!!!

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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