Fall 1998, Math 100
CHAPTER 7

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

Due 11/18 at 8am, assigned 11/16

Section 7.1: Introduction to the Trigonometric Functions

• To read: Section 7.1: pp 425-429
• Be sure to understand: What a unit circle is. How the unit circle is used to develop the graphs of sin(theta) and cos(theta). The relationship between the triangular definitions of sine and cosine given at the beginning to the circular definitions mainly focused upon.
1. Consider a 3-4-5 right triangle (5 is of course the hypotenuse). Let x be the angle opposite the side of length 3. Find
1. sin(x)
2. cos(x)
2. What is sin(0o)?
3. What is sin(90o)?
4. What is cos(0o)?
5. What is cos(90o)?
No matter how much or little you understood of the reading, you should be able to figure these values out!
• E-mail Subject Line: Math 100 Your Name 11/18

Due 11/20 at 8am, assigned 11/18

Section 7.1: Introduction to the Trigonometric Functions

• To read: Section 7.1: p. 430-end
• Be sure to understand:the meaning of the notation cos2x and sin2x--what is being squared? Where THE MOST IMPORTANT relationship comes from. What a radian is.
1. What is THE MOST IMPORTANT relationship between the sine function and the cosine function?
2. What does the graph of THE MOST IMPORTANT relationship (in all of trigonometry) look like??
3. Why do we need radian measure?
4. Convert 120o to radian measure.
• E-mail Subject Line: Math 100 Your Name 11/20

Due 11/23 at 8am, assigned 11/20

Section 7.2: Trigonometric Functions and Periodic Behavior

• To read: Section 7.2: all
• Be sure to understand: where the numbers are coming from in the daylight in San Diego example (the vertical shift, amplitude, period, and horizontal shift).
1. How many hours of daylight are there in San Diego on December 21?
2. What does that number represent on the graph of H(t)?
3. How does the graph of f(x)=sinx+5 differ from the graph of sinx?
4. How does the graph of g(x)=2cosx differ from the graph of cosx?
• E-mail Subject Line: Math 100 Your Name 11/23

Happy Thanksgiving!

Due 11/30 at 8am, assigned 11/23

Nothing!

Due 12/2 at 8am, assigned 11/30
Section 7.3: Relationships Between Trigonometric Functions

• Reminder: The gateway is/was yesterday, 12/1. Be sure to take it!
• To read: Section 7.3: all
• Be sure to understand: why cos(x)=cos(-x), and why the cosine function is said to be even; why sin(x)=-sin(x), and why the sine function is said to be odd. Check on your graphing calculator (use the computer's graphing calculator if you don't have one, or borrow a friend's): graph sin(2x) and 2sin(x)cos(x) on the same graph; graph cos(2x) and cos2(x)-sin2(x) on the same graph. Understand why these are called identities. Also understand example 1.
1. Simplify sin(x)+sin(-x).
2. Simplify cos(x)+cos(-x).
3. Write cos(3x) using only cosines and not including any multiple angles.
• E-mail Subject Line: Math 100 Your Name 12/2

Due 12/4 at 8am, assigned 12/2

Section 7.4: Solving Trigonometric Equations: The Inverse Functions

• To read: Section 7.4: all
• Be sure to understand:the restriction of the domain for arcsine and arccosine.
1. On what day (not the day of the year, simply the number of the day) will San Diego have 11 hours of daylight?
• E-mail Subject Line: Math 100 Your Name 12/4

Due 12/7 at 8am, assigned 12/4

Section 7.5: The Tangent Function

• To read: Section 7.5: all
• Be sure to understand: the definition of the tangent function; how it fits with the triangle trig definition of tangent: tan(x)=opp/adj; why and where the graph of tangent has vertical asymptotes; what secx, cscx, and cotx are.
1. Evaluate tan(pi/4) without a calculator.
2. Evaluate tan(pi) without a calculator.
3. Explain why tangent has a vertical asymptote at x=pi/2.
• E-mail Subject Line: Math 100 Your Name 12/7

Due 12/9 at 8am, assigned 12/7

Review Chapter 7

• To read: Review Chapter 7
• Be sure to understand: all, of course
1. Evaluate sin(11pi/3) without a calculator.
2. Give the frequency, period, amplitude and phase shift for y=5-2cos(3/4(x)+pi).
3. Is sin3x+cos3x=1 an identity? Decide by looking at the graph. If not, find a point graphically that lies on both. If so, prove it algebraically.
4. Solve for x in -4sin(x)=6cos(x). You may use your calculator.
• E-mail Subject Line: Math 100 Your Name 12/9

Have a wonderful 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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