Overview Schedule of Assignments Honor Code

Please be brief but clear in your answers to each of the following. Be alert to going back to the fundamental meanings of angle measure, sin( ), and cos( ) whenever it will help to construct a coherent explanation.

1.       Graph sin(x), -10 < x < 10; answer a-d.

a)       What does x stand for?

b)      What does "sin(x)" mean for some specific value of x?

c)       What does a point on the cartesian graph of sin(x) stand for?

d)      Why does the cartesian graph of sin(x) appear as it does?

2.       Jimmy said, "I found a neat trick. sin( ) has a period of 2pi, which means that it repeats itself whenever whatever is in the parentheses varies by 2pi. So, sin(5+3x) is periodic whenever 5+3x varies by 2pi."

Is Jimmy correct to think this way?

How would Jimmy use this insight to explain the behavior of

a)       y = cos(40x)

b)      y = cos(x2)?

3.       Explain the behavior of y = a sin(x) in a way that, with very little modification, your explanation also works for explaining the behavior of y = cos(x)sin(x).

4.       Explain the behavior of y = cos(sin(x)). Then use this as the basis for explaining the behavior of

y = cos(a sin(x)), 0 < a < 10

5.       Consider the function g(x) = cos(x)+|max(0,min(tan(100x),0.01))|.

1. Describe the behavior of g(x) as it appears with no further investigation.
2. Use SHIFT-DRAG to zoom in on a small part of the graph. Would you give the same description of the graph's behavior that you gave in part (a)? Why?
3. Explain the behavior of g(x).

6.       Examine each function's behavior as |x| becomes very small and as |x| becomes very large. Why do these behave as they do?

7.       Make up a question about a trig function that will lead students' explorations and provoke some insight into an interesting idea. Give an "excellent" answer to your question.

 Overview Schedule of Assignments Honor Code