At 13:04 12/10/98 PST, you wrote: >Hello. My name is Natalie Kunz and I'm a student at Marquand-Zion high >school in Missouri. >For Trigonometry class, we have to do projects on how trig relates to >the "real world." >Since marine biology is way interesting, I decided to see how scientists >use sine and cosine curves to help track whales. >DO scientists use sine curves? > Hi, Natalie (how did you pick "blondechicken" for your email name?). The questions are certainly getting interesting this year. Let's see, sine curves and whale-tracking? How's this for a stretch - a sound underwater is actually a wave of pressure that varies with time that follows a sine curve if you can look at it with the right equipment. Scientists using the Navy's submarine tracking stations have been able to follow whales in the middle of the ocean by listening to their sounds from a room in Virginia. That may be stretching a point to answer your question, but in fact many aspects of marine science (or any science) involve trigonometry (and not just sine functions). Many of the terms in the equations that describe how waves form or how currents flow include trigonometric functions (of course I forgot all of them the day after I took my last exam in physical oceanography). Mathematics is the language of science, and no one can be a successful scientist any more without some understanding of math. Maybe biologists might use less math than astrophysicists, but we still need to know the basics. Here's what I use trig for most often - studying whales often involves going out to sea on a ship and working with the data later. We use a variety of navigation equipment to tell where we are, and we keep track of that using latitude and longitude. Many times I want to know the distance between two locations (for example, how far did whale number 1163 move from the spot where we attached the radio tag to where we saw her again three days later). The formula for calculating the distance (in nautical miles) from point 1 to point 2 when you know the latitude and longitude of both is: 60 arcos[sin(lat1) sin(lat2) + cos(lat1) cos(lat2) cos(lon2 - lon1)] Easy as pie, right? I actually use that a lot, except I copied it from a book into a computer program, so I don't have to really know it. But there is something much simpler that I also use frequently - when I want to know something about distances but don't have my computer. Do you know why sailors (and airplane pilots, too) use different miles than the ones we use on land (nautical miles instead of statute miles)? It's because a nautical mile really means something - it is 1/5400th of the distance from the equator to the north pole. Since that is 90 degrees of latitude and each degree contains 60 minutes, one nautical mile equals one minute of latitude. It also equals one minute of longitude, but only at the equator. If you look at a globe, the longitude lines get closer together the farther you get from the equator, until they all meet at the poles. So how long is one minute of longitude at any place other than the equator? What function describes how the longitude lines get closer when you go from a latitude of 0 degrees to a latitude of 90 degrees? COSINE! Cosine(0) = 1.000 and cosine(90) = 0. The cosine of the latitude tells you the length of a minute of longitude anywhere on Earth. I'm sitting right now in an office at latitude 41 degrees, 29 minutes, 28 seconds North, the cosine of that is 0.7490585109 (approximately), and one minute of longitude here is about three-quarters of a nautical mile (1,387 meters). Cheers, Dr. Bob =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= | Robert D. Kenney, Ph.D. rkenney@gso.uri.edu | | University of Rhode Island | | Graduate School of Oceanography | | Bay Campus - Box 41 TEL: (401) 874-6664 | | Narragansett, RI 02882-1197, U.S.A. FAX: (401) 874-6497 | =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=