Trigonometry Webquest

Lee Stiff, president of the National Council of Teachers of Mathematics, says there is merit in having projects that "engage students and get them to delve deeper into the mathematics and the sciences and such relationships as mathematics and social studies or mathematics and history. Those kinds of projects are worthwhile because they show young people that math is connected to a world outside itself and that mathematics can be useful."

Graphing Trig functions

Your Task

For your major quarter project, you will write a letter to a student, such as yourself a few weeks ago, explaining the methold of graphing any trigonometric function. Use the unit circle as your reference. Topics to be covered must include the following:

1. Basic shapes of the 6 trig functions (make sure you carefully define and describe each one.) Include a description of period, domain and range for each function. Also include discussion of a reflection on a graph.

2. Transformations

a. Amplitude, period change, vertical shift, and phase shift on the sine funtion
b. Vertical stretch, phase shift and period change on the tangent function
c. Vertical stretch, secant function

3. Addition of ordinates

4. Multiplication of ordinates

5. Comparisons and contrasts among the functions

6. Choose to describe either

a. an application of a trig function
b. a career that uses trig
c. an interesting problem that uses trig for a solution.

Careers in Trigonometry

Introduction - A student asks which careers use trigonometry:

From the Mathforum.Org: 

When my wife and I were taking calculus, we said to
him that you can approximate any curve as a series of small triangular
steps.  "You mean like this?" he asked.  He showed us how he does it
with a compass and ruler.  Framing homes, finishing cabinets, you name
it, everything he does is applied math.  Roofs are trusses and trusses
are series of triangles.  Roofs are critical where snowfall from "lake
effect" can be five feet or more overnight, regularly and predictably.

My father was a Tool and Die Maker for the Boeing Airplane Co. for more than
25 years.  While I was in college, I visited him at work one summer.  He was
"just" a blue collar worker and I was the big math major.  But he explained
how he did what he did.  It was all with trig and real mathematics. He
created the parts (the tools) that would make the parts for all of the early
airplanes.  If you needed a bolt that would screw in 6 inches in 4.5 turns,
he would create the tool to create the bolt.  Imagine if you can unwind the
bolt's threads.  He formed a triangle that uses trig to determine the angle
of the threads from the length of the shaft and the diameter of the bolt.  I
suddenly was very impressed with all the real math that my blue collar
father knew.  Trig is not just for math teachers and mathematicians - but
then again, he was a mathematician...

 From Ask an Astronomer

Probably the biggest impact that trigonometry has had in Astronomy is in the finding of 
distances to nearby stars through the method of parallax. As you know, the Earth orbits 
around the Sun once a year. This means that at six month intervals the Earth is looking 
at a star from the two corners of an isosceles triangle (where the point is at the star). 
We can observe how far the star appears to move against the background galaxies in that 
time and find the angle of the triangle from that. With the angle and the length of the 
base (the diameter of the Earth's orbit) we can find the height of the triangle - or the 
distance to the star. 

The movement of the star against the background as we orbit the Sun is called its parallax. 
In fact you've probably observed parallax when you travel in the car. You might notice that 
the nearby bushes (or other objects) along the road appear to move with respect to more far 
away things as you travel along the road. You can also observe the parallax of your thumb 
if you hold it at arm's length and look at it with alternating eyes shut. Again, it should 
appear to move with respect to the background. If you knew the distance between your eyes 
and could measure the angle your thumb appeared to move by you could find out the length of 
your arm by doing this.
   

Careers In Trigonometry Links to Explore:

List of Careers
Math Association of America
Math Science Career Information
Careers in Cartography
Industrial Careers

Description of all careers: Occupational Outlook Handbook

Your Product

This paper must be created in conversational English. Although some diagrams and mathematical examples may be necessary, the paper should be primarily prose.

Assessment

Grading Considerations

1. Accuracy of facts -- no errors.
2. Completeness of important details -- no omissions.
3. Demonstration of your understanding of the concepts.
4. Clarity of thought
5. Originality of the problems you select.
6. There are no length requirements.