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	Precalculus Functions and Graphs 4/e Barnett/Ziegler/Byleen
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Exercise 1:
Adding and subtracting vectors is easy... But, seeing what is going on geometrically can be more challenging. Try adding and subtracting several sets of vectors at the Graphing Vector Calculator. You can enter in the vectors by drawing them with your mouse or you can type your desired values in the appropriate boxes. Keep a record of your work by drawing the vectors by hand.

Exercise 2:
Polar coordinates have some very important uses. One of the most important is in the field of Astronomy. In your text, you learned about polar coordinates in two dimensions... But, we live in three dimensional space. This NASA site, Maps of the Heavens, gives a nice history of the Cartesian coordinate system as well as the polar system and shows how polar coordinates are used in three dimensions. (They are called spherical coordinates in 3-D.) Answer the following questions:

1)	Which angle, the azimuth or the elevation, do you use in two dimensions?
2)	When astronomers chart a heavenly body, what terms do they use for the azimuth and elevation?
3)	What do astronomers use for "zero" when measuring the azimuth and the elevation?

Exercise 3:
Art and mathematics aren't as far apart as you might think. (Remember the awesome pictures you generated back in our Chapter 2 exercises with complex numbers?) Artistic MathGV(tm) Graphs is a collection of art created using trigonometric and polar graphs. Some of these may remind you of that old Spirograph set you had when you were a kid! Grab a couple of trig graphs and create your own piece of artwork.

Here's another great math/art site that combines trigonometry and fractals: SineArt.

Exercise 4:
Now that you've mastered trigonometry, you can get a global view of why you need trig and how it is used at Applications of trigonometry. You will also get to see a little preview of Calculus.

Chapter 7: Additional Topics in Trigonometry