4.4. May 14, 2002: Letter to Zap #1

"A mathematician is a machine for turning coffee into theorems."--Paul Erdös

Caveat Lector: This is a web-friendly version of the activity sheet LETTER TO ZAP #1, sans graphics. A scan may become available at a later date.

COORDINATE SYSTEMS: LETTER TO ZAP #1

Zap is confused about coordinates and conversions. You are going to write a letter to explain some of it.

You and your partner each have a card with the same point. It might look like this:

         polar-to-Cartesian

            r  theta

         A (1, 30 degrees)

In your letter, which you will both write together, you will include these things:

Draw diagrams to explain how polar coordinates work
Draw diagrams to explain how Cartesian coordinates work
Graph the point (you'll need polar graph paper)
Show how to estimate the conversion on your card (polar-to-Cartesian or Cartesian to polar)
Show how to do the exact conversion

polar-to-Cartesian hints:
sin(theta) = y/r
cos(theta) = x/r

Cartesian-to-polar hints:
r^2 = x^2 + y^2
theta = arctan(y/x)

You can use words, diagrams, graphs, pictures, comics, color--whatever you need to help Zap understand.

BE POLITE!
BE CONSTRUCTIVE!