Use the rules 𝑑 𝑑𝑥sin(𝑥) = cos(𝑥) and 𝑑 𝑑𝑥sin(𝑓(𝑥)) = 𝑓′(𝑥)cos(𝑓(𝑥)).

mm-u3-t2-s1-d1

Interactive

The slopes of sin x trace out cos x

manipulative

Sweep a tangent along y = a sin(bx+c)+d or a cos(bx+c)+d; every slope you measure is plotted below and the dots build the derivative graph.

Open fullscreen →

Want a different take?

Already have one and want another angle on this point? Describe what students should notice. Requests are read and acted on.