# Derivative of Sine & Cosine Functions (Quick Investigation)

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 .