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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+3*x*) is periodic whenever 5+3*x* varies by 2pi."

Is Jimmy correct to think this way?

How would Jimmy use this insight to explain the behavior of

a)
*y* = cos(40*x*)

b)
*y* = cos(*x ^{2}*)?

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))|.

- Describe the behavior of
*g*(*x*) as it appears with no further investigation. - 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?
- 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 |