There are many applications of trigonometry in everyday life. One of these is the position of anything on the earth. You have undoubtedly heard of latitude and longitude. These are coordinates defined on the earth’s surface that provide the position of a point, much like defining the position of a point on a cartesian coordinate system ( see my posts on Graphing). As of this writing, my position is -37.6836353 latitude and 144.746533 longitude. A more traditional way to express this location is 37° 41′ 1.086” S, 144° 44′ 47.5182” E. Notice that in the second way, the degree symbol is used. This is because latitude and longitude are angles. I’ll explain that in a minute.
Also notice that in the second method, that there are the symbols ‘ and ”. These mean “minutes” and “seconds” respectively. Just like hours, a degree is split into 60 minutes, and each minute is is divided into 60 seconds. So one difference between the using two methods is whether you want to use minutes and seconds for parts of a degree or decimals. This is the same as saying the time is now 9 hours, 4 minutes, 40 seconds or 9.0778 hours
Another difference between the two methods is that the first uses negative and implied positive signs while the second uses S and N for latitude and E and W for longitude. For latitude, S means South and N means North. For longitude, E means East and W means West.
So how are these angles measured? The below graphic helps explain these angles:
Let’s first look at longitude. This angle is frequently represented with the greek letter phi, ϕ. Imagine circles around the earth that pass through both poles. These are called great circles as they are the largest circles that can be drawn on the earth’s surface and divide the earth into two hemispheres (assuming that the earth is a perfect sphere). One of these circles was designated as a reference circle called the prime meridian. This reference circle was finally (after a history of development) agreed upon in 1884. It is designated as the 0° circle of longitude on the side that passes through Greenwich, England. Other great circles, like the one in red above, are an angle away from the prime meridian. One can go east (positive) from this reference circle or west (negative) until you get to the other side of the prime meridian. So the largest longitude angles are ±180°. Let’s now look at latitude.
The latitude angle is often represented with the greek letter lambda, 𝝀. The reference for this angle is a much more natural geometric one, the equator. The equator is 0° latitude. Along any great longitude circle, like the one in red above, one can go north (positive) or south (negative) to form an angle with the equator, measured at the earths centre like longitude. So the largest latitude angles are ±90° which are the poles.
Now before GPS and other navigational aids, it was a real trick to know your position on earth. Longitude was particularly tricky, but measuring latitude was very possible. How that was done, will be the topic of my next post.