Mathematics 133 – Intensive Calculus for Science 1 Discussion 6 – Derivatives of Trigonometric Functions October 28, 2005

Background

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

\frac{d}{dx} sin(x)  and  \frac{d}{dx} cos(x)

Discussion Questions

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.

B) Repeat the process from question A, but estimating f′(0) for f(x) = cos(x)

C) Here is an accurate scale drawing of y = sin(x) for 0 < x < 4π Use it to sketch the graph of the derivative function of sin(x) Any guesses about which function this is?