**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.

**Reading questions:**

- 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
- sin(x)
- cos(x)

- What is sin(0
^{o})? - What is sin(90
^{o})? - What is cos(0
^{o})? - What is cos(90
^{o})?

No matter how much or little you understood of the reading, you should be able to figure these values out! - 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
**E-mail Subject Line:**Math 100 Your Name 11/18

**To read:**Section 7.1: p. 430-end

**Be sure to understand:**the meaning of the notation cos^{2}x and sin^{2}x--what is being squared? Where**THE MOST IMPORTANT**relationship comes from. What a radian is.

**Reading questions:**

- What is
**THE MOST IMPORTANT**relationship between the sine function and the cosine function? - What does the graph of
**THE MOST IMPORTANT**relationship (in all of trigonometry) look like?? - Why do we need radian measure?
- Convert 120
^{o}to radian measure.

- What is
**E-mail Subject Line:**Math 100 Your Name 11/20

**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).

**Reading questions:**

- How many hours of daylight are there in San Diego on December 21?
- What does that number represent on the graph of H(t)?
- How does the graph of f(x)=sinx+5 differ from the graph of sinx?
- How does the graph of g(x)=2cosx differ from the graph of cosx?

**E-mail Subject Line:**Math 100 Your Name 11/23

**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 cos^{2}(x)-sin^{2}(x) on the same graph. Understand why these are called*identities*. Also understand example 1.

**Reading questions:**

- Simplify sin(x)+sin(-x).
- Simplify cos(x)+cos(-x).
- Write cos(3x) using only cosines and not including any multiple angles.

**E-mail Subject Line:**Math 100 Your Name 12/2

**To read:**Section 7.4: all

**Be sure to understand:**the restriction of the domain for arcsine and arccosine.

**Reading questions:**

- 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

**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.

**Reading questions:**

- Evaluate tan(pi/4) without a calculator.
- Evaluate tan(pi) without a calculator.
- Explain why tangent has a vertical asymptote at x=pi/2.

**E-mail Subject Line:**Math 100 Your Name 12/7

**To read:**Review Chapter 7**Be sure to understand:**all, of course

**Reading questions:**

- Evaluate sin(11pi/3) without a calculator.
- Give the frequency, period, amplitude and phase shift for y=5-2cos(3/4(x)+pi).
- Is sin
^{3}x+cos^{3}x=1 an identity? Decide by looking at the graph. If not, find a point graphically that lies on both. If so, prove it algebraically. - Solve for x in -4sin(x)=6cos(x). You may use your calculator.

**E-mail Subject Line:**Math 100 Your Name 12/9

CHAPTER 7

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

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

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

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

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

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

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

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

Back to: Precalculus | My Homepage | Math and CS