course Mth 164 ̅wxKƶLݐassignment #002
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13:51:33 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)= - cos 1/4 = - 1/4 f(a) + f(a+2pi)+f(a-2pi) = 1/4 + 1/4 + 1/4 = 3/4 confidence assessment: 2
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13:53:15 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 --> The value of f(a) + f(a+2pi) + f(a-2pi) is 3*f(a) essentially because it is known that f(a+2pi) = f(a) and that f(a-2pi) = f(a) also, so the result is f(a)+f(a)+f(a). confidence assessment: 3
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13:53:22 query (no summary needed)
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RESPONSE --> confidence assessment:
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13:55:01 How does the circular model demonstrate the periodic nature of the trigonometric functions? Be specific.
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RESPONSE --> The circular model demonstrates the periodic nature of the trigonometric functions because the resulting graph follows a point moving around the circle at a constant speed, this produces maximum and minimum values (peaks) that occur at a frequency dependent on the linear speed of the point circling the circle, the sine function is the y value on the circular graph for example, when the point revolves around, the sine function can be graphed by the changing y values over a period of time. confidence assessment: 2
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13:56:40 How does the circular model demonstrate the even or odd nature of the sine and cosine functions? Be specific.
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RESPONSE --> The even or odd nature of the sine and cosine functions are demonstrated by the circular model becuase if theta is reflected over the x axis standard position and becomes - theta then there are points (x,y) for theta and points (x, -y) for negative theta, therefore sin theta = y and cos theta = x becomes sin (-theta) = -y and cos (-theta) = x. confidence assessment: 3
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13:56:58 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 --> Yes, I have memorized the lovely unit circle. confidence assessment: 3
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13:57:03 Comm on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> confidence assessment:
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