## 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." |

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.

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.

Description of all careers: Occupational Outlook Handbook

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.

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