query_2

course MTH174

??????????????assignment #002

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002.

Precalculus II

06-18-2007

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20:55:52

query ch. 5.2 # 102 f(x) = cos(x), f(a) =1/4, find f(-a), f(a) + f(a+2`pi) + f(a - 2 `pi)

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RESPONSE -->

f(-a), f-1/4

f(a) + f(a+2`pi) + f(a - 2 `pi)

f(1/4) + f(1/4 + 2 `pi) + f(1/4 - 2 `pi)

f(3/4)

confidence assessment: 3

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20:56:51

What is the value of f(a) + f(a+2`pi) + f(a - 2 `pi) and how did you use the even-odd and/or periodic properties of the function to obtain your result?

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RESPONSE -->

3/4, the + and - 2 `pi, cancels out

confidence assessment: 3

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20:58:31

How does the circular model demonstrate the periodic nature of the trigonometric functions? Be specific.

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RESPONSE -->

Certain points display how the functions are based on pi, and equalateral theroies

confidence assessment: 3

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22:46:12

How does the circular model demonstrate the even or odd nature of the sine and cosine functions? Be specific.

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RESPONSE -->

confidence assessment: 0

** The answer can be pictured in terms of 2 ants, one going counterclockwise and the other clockwise.

The cosine is the x coordinate of the reference point. Since we start at the positive x axis, it doesn't matter whether we go clockwise or counterclockwise through the given angular distance, we end up with the same x coordinate.

the sine function being the y coordinate, clockwise motion takes us first to negative values of the sine while counterclockwise motion takes us first to positive values of the sine. This image shows why the sine is odd. **

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22:48:56

Can you very quickly sketch on a reference circle the angles which are multiples of `pi/6 and immediately list the sine and cosine of each? Can you do the same for multiples of `pi/4? (It's OK to answer honestly but be prepared to have to do this on a test, and remember that this task is central to understanding the trigonometric functions; if you've reached this point without that skill you have already wasted a lot of time by not knowing something you need to know to do what you're trying to do).

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RESPONSE -->

I'm 90% confident that I can.

confidence assessment: 3

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22:50:00

Comm on any surprises or insights you experienced as a result of this assignment.

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RESPONSE -->

I honestly can't explain the on question that I skipped, but I am getting an understanding of the functions.

confidence assessment: 3

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See my notes and let me know if you have questions. &#