In my previous post, I presented a non-algebraic approach to exploring the slope of the sine function. That method involved placing a secant line on the graph and then dragging the two points that defined the line as close together as possible to approximate the tangent line.

By dragging, you were able to bring the two points reasonably close, but without finer control, you could not bring the two points arbitrarily close, say within a distance of 0.0001. To achieve that level of precision, you’re going to create a parameter, h, that you’ll use to set the distance between the two points on the secant line. This method provides a meaningful introduction to the symbolism used to represent the derivative of a function, but still without diving directly into the formal algebra.

To explore this approach, use the websketch below (and here). This worksheet provides the details, and the video at the end of this post demonstrates the steps.