Exploring gradient of y=sin kx - Geogebra Investigation

This is an interactive GeoGebra page. You can use the online version here without downloading anything if you like.

It is a similar sort of idea to the “Introducing e^x”, which has a full description on my blog. I’ll summarise quickly how to use this one…

1. Display the graph of y=sin kx with k=1 and ask them to draw the gradient function. They may guess that it looks like y=cosx

2. Display the gradient function by clicking on the checkbox. Try some different values of k, and notice how the “amplitude” of the gradient function increases.

*You can zoom in with just the x-axis by holding down Shift and click-dragging a point on the x-axis. *

1. Try different values of k. You will find that and k=~57, the gradient function is pretty close to cosine.

2. There is a secret checkbox next to the “Show y=f(x)” checkbox, which will reveal the y=cos(kx) graph. Display it and zoom in on the two graphs which seem to overlap.

3. Adjust the value of k and zoom in, repeatedly so that you improve the accuracy of k. You will find that the k-value is around 57.2957795.

4. Ask students to reflect on what they just saw. You want them to realise that when angles are measured in radians, the gradient of y=sin x is y=cos x, and that unless the angle is measured in radians, this is not true.

I hope this makes sense and it is useful for you. If you have ideas for using this which I haven’t written about or ideas for making it better please get in touch.