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Material:
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Mathematical Visualization Toolkit
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| Submitted by: |
David Fink on Jun 11, 2008 |
| Date Last Modified: |
Jun 11, 2008 |
| Title: |
Graphing Trig Functions |
| Description: |
Students will be graphing a variety of sine and cosine curves to discover where the amplitude and frequency are located in a trig function. Students will then try to characterize how the amplitude and frequency affect the graphs of trig functions. |
| Type of Task: |
Group,
Supervised
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| Time Required |
20 - 30 minutes |
| Topics: |
Trig Functions: Sine and Cosine Curves |
| Course: |
Trigonometry |
| Audience: |
High School
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| Categories: |
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| Prerequisites Skills: |
- General knowledge of graphing a function.
- General knowledge of setting up an appropriate domain and range for a function
- Shape of a sine and cosine curve.
- General knowledge of how to plot a function on the Mathematical Visualization Tool. |
| Learning Objectives: |
- Students will be able to graph a variety of sine and cosine curves on a given domain.
- Students will be able to find the amplitude and frequency of a cosine curve.
- Students will understand how the amplitude and frequency affect the graph of a sine and cosine function. |
| Technical Notes: |
- Students should have at least one computer for every two students in the classroom.
- Computers need to have internet access. |
| Text of Learning Exercise: |
Directions: Graph each of the following sets of functions using the Mathematical Visualization Toolkit Plot Program. Use the overlay option to put each set of functions on one plot. Make sure to use a domain of 0 < x < 2pi and a range of -3 < y < 3.
Objectives:
1) Define how the coefficient of the function affects the graph of the function.
2) Define how the coefficient of x affects the graph of the function.
3) Print out each plot you make and label the label the functions that were plotted(defining a color for each function will help to distinguish between functions)
Set 1: y = cos(x), y = 2cos(x), y = 3cos(x)
Set 2: y = .5sin(x), y = 3sin(x), y = 1.5sin(x)
Set 3: y = cos(x), y = cos(2x), y = cos(3x)
Set 4: y = sin(x), y = sin(.5x), y = sin(2x)
Set 5: y = 2cos(2x), y = 3sin(2x), y = 3cos(.5x) |
| Assessment: |
Given: y = .5cos(2x)
a) Describe what this graph will look like without plotting this function. |
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