Tuesday HW!

Tonight, please complete the investigation that we started in class! If you were out, you will have to complete this on your own--start now! Remember, this will be collected and graded, so get it done!

• For the last question, you have to come up with a formula to calculate period...this counts as extra credit! Take a look in section 4.5 of your book to find an answer!

Tomorrow in class we'll talk about what we discovered--amplitude, period, etc.

For those who were out (or lost their papers), here's the investigation that will be collected and graded:

Graphing Exploration Part 1

Directions: Use your graphing calculator to answer the following questions about the graphs of sine and cosine.

1) What happens when we multiply sin(x) by a constant (we will call a)? Use your graphing calculator to graph f(x)= a sin(x) and f(x)= a cos(x) for the situations given in parts a-d.

a)      Describe what happens when a is greater than 1 (a > 1). (Choose a value bigger than 1…like 2! Now, graph y = 2sinx and compare this to the graph of y=sinx –how did the “2” affect the graph?)

b)      Describe what happens when a is equal to -1 (a = -1).

c)      Describe what happens when a is less than -1 (a < -1).

d)      Describe what happens when a is in between 0 and 1 ( 0 < a < 1). .

e)      Write a general rule about how a affects the graph of f(x)=a sin(x) or f(x)= a cos(x). Be sure to reference your findings from parts a-d above. (3 points)

2) What happens when we multiply our input (angle) by a constant (we will call b). Use your graphing calculator to graph f(x)= sin(bx) and f(x)= cos(bx) for the given situations in parts a-

a)      Describe what happens when b = 2. (That is, graph sin(2x) or cos(2x) and explain how the graph changes.)

b)      Describe what happens when b = 4

c)      Describe what happens when b = 1/2

d)      Describe what happens when b = 1/4

e)      Write a general rule about how b affects the graph of f(x)= sin(bx) or f(x)= cos(bx). Be sure to reference your findings from parts a-d above. (2 points)

Type 2 Writing: Graphing Exploration (Part 1)

1. The constant a is known as the amplitude of a trigonometric function. In your own words (and in complete sentences), define amplitude. (2 points)

2. The constant b helps us to find the period of a trigonometric function. In your own words (and in complete sentences), define period. (2 points)

3. Use the information below to write an equation we can use to find the period of a trigonometric function based on b, the coefficient to x (our angle measure). (2 points)