# Derivace funkce sinus a cosinus

In the applets below, graphs of the functions and are shown.
In each applet, drag the BIG WHITE POINT along the graph of the displayed function.
The y-coordinate of the point being traced out = the slope of the tangent line to the graph of f.
Interact with each applet for a few minutes, then answer the questions that follow.

## 1)

Based on your observations, if , can you write an expression for ?

## 2)

Based on your observations, if , can you write an expression for ?

## 3)

Use the limit-definition of a derivative to prove that if , then .

## 4)

Use the limit-definition of a derivative to prove that if , then .