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\centerline{Mathematics 133 -- Intensive Calculus for Science 1}
\centerline{Discussion 6 -- Derivatives of Trigonometric Functions}
\centerline{October 28, 2005}
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{\it Background}
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We now know how to differentiate powers $x^n$, exponentials $a^x$, 
and functions made up from these by products, quotients, and 
compositions.  Our next goal is to learn about the derivatives
of trigonometric functions.  In the discussion today, we will 
look at some preliminary observations about 
$${d\over dx} \sin(x) \qquad {\rm and} \qquad {d\over dx} \cos(x)$$
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{\it Discussion Questions}
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A)  What limit would you need to compute to find
$f'(0)$ for $f(x) = \sin(x)$?  Investigate this limit
numerically by making a table of values for the 
difference quotient at $h = -.1, -.01, -.001, .001, .01, .1$.
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B)  Repeat the process from question A, but estimating
$f'(0)$ for $f(x) = \cos(x)$
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C)
Here is an accurate scale drawing of $y = \sin(x)$ for $0 < x < 4\pi$
Use it to sketch the graph of the derivative function of $\sin(x)$
Any guesses about which function this is?
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