Derivace funkce sinus a cosinus
- Author:
- Šárka Voráčová, Tim Brzezinski
- Topic:
- Calculus, Cosine, Derivative, Functions, Sine, Trigonometric Functions
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 .
Formal proof with limits.
