A2.4

determine, through investigation using technology, the graph of the derivative $f^{\prime }(x)$ or $\frac{dy}{dx}$ of a given sinusoidal function [i.e., $f(x)=\sin x$, $f(x)=\cos x$] (e.g., by generating a table of values showing the instantaneous rate of change of the function for various values of $x$ and graphing the ordered pairs; by using dynamic geometry software to verify graphically that when $f(x)=\sin x$, $f^{\prime }(x)=\cos x$, and when $f(x)=\cos x$, $f^{\prime }(x)=-\sin x$; by using a motion sensor to compare the displacement and velocity of a pendulum)