Derivation of sine

Task

Create an applet with the sine function and graph its derivative through the slope of the tangent in each point.

Move point A along the function graph and make a conjecture about the shape of the path of point S, which corresponds to the slope function.
Turn on the trace of point S. Move point A to check your conjecture. Hint: Right-click point S (MacOS: Ctrl-click, tablet: long tap) and select Show Trace.
Find the equation of the resulting slope function and enter it into the Input Bar using g(x) = ... . Move point A along the graph of function f. If your prediction is correct, the trace of point S will match the graph of your function g.

1.		Enter the function `f(x) = sin(x)`.
		Right-Click on the Graphics View and select Graphics... . Select tab xAxis and change the unit to
2.		Create a new point A on function f. Hint: Point A can only be moved along the function.
3.		Create tangent g to function f through point A.
4.		Create the slope of tangent g using the Slope tool.
5.		Define point `S = (x(A), m)`. Hint: `x(A)` gives you the x-coordinate of point A.
6.		Connect points A and S using a segment.
7.		Turn on the trace of point S. Hint: Right-click point S (MacOS: Ctrl-click, tablet: long click) and select Show Trace.
8.		Right-click (MacOS: Ctrl-click, tablet: long click) point A and choose Animation from the appearing context menu. Hint: An Animation button appears in the lower left corner of the Graphics View. It allows you to either pause or continue an animation.