Investigating the Derivative of Sin and Cos
GROUP MEMBERS:
1. _____________________________
2. ______________________________
3. ______________________________
4. ______________________________
Goal: Use the graphical interpretation of derivative (slope of the tangent line) to
investigate the derivative of sin(x) and cos(x).
Roles:
Person 1: Questioner
Person 2: Reader
Person 3: Manager
Person 4: Presenter.
Instructions:
1. y = f(x) = Sin(x).
a. For each of the x values given in the table, sketch the tangent line to the graph through the point
(x, Sin(x)) and then enter the value of the slope in the table. Start with Person 1 and take turns.
x
- " /2
0
slope m at x
" /2
"
3 " /2
2"
1
!
!
!
!
!
b. Person 2: Plot the points (x, slope at x) from the table on the following graph. Person 3: Then
“connect the dots”.
c. Group: What do you think
!
d
sin(x) equals?
dx
2. y = f(x) = Cos(x).
a.For each of the x values given in the table, sketch the tangent line to the graph through the point
(x, Cos(x)) and then enter the value of the slope in the table. Start with Person 3 and take turns.
x
- " /2
slope m at x
1
!
0
!
" /2
!
"
!
3 " /2
2"
!
b. Person 4: Plot the points (x, slope at x) from the table on the following graph. Person 1: Then
“connect the dots”.
c. Group: What do you think
!
d
cos(x) equals?
dx