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