is a term that may strike unease in some hearts.  The simplest definition of this branch of Mathematics is “the study of angles and triangles.”  However, the study of trigonometry is a whole lot more than that; more comprehensive and complex.  Trigonometry has applications throughout the world, including construction, geography, physics, acoustics, medicine, meteorology, and navigation, just to name a few.  To begin the descent into “trig,” let’s begin with that original, simple definition of studying angles.

 is an instrument used today that was invented in the circa neighborhood of 1730.  This country was a collection of colonies, the Ottoman-Persian War began, and mad king George’s father, George, was in charge of the English Empire.  Sextants were sophisticated tools at the time, measuring the angular elevation of stars so that a navigator could determine a ship’s current latitude.  

 lines were defined as circles parallel to the equator.  Angles were “drawn” by the device in relation to the Equator, and the measurement of these angles indicated the location of the ship.  The value of the measurement was communicated and translated into positional language, all based on angles.

Angles may harken back to days long past spent studying Geometry.  Relative to measurement, angles have both positive and negative values.  The 

 of an angle involves the vertex sitting at the origin on a plane and the side of an angle stretching straight forward known as the 

.  The side that rotates from the origin and the initial side forms the 

.  When the terminal side rotates counter-clockwise, a positive angle is formed.  Conversely, if the side rotates clockwise, a negative angle measurement is reported.

Furthermore, the degrees that are used primarily to measure angles comes out of ancient history.  The Babylonians used a system of 60, rather than the modern system of 10, to define a regular amount.  Thus, the equilateral, equiangular triangle was given the exact measure of 60°.  (1/60) of this angle was then defined as 1°.  No surprise there.  If you take that value of 1° and divide it further by 60, you get 

Based on the definition of degrees, minutes and seconds, how would you translate the following measurements of latitude using minutes and seconds, and just in degrees?

North Latitude: 15.735° into degrees, minutes and seconds

North Latitude: 39° 5' 34" into degrees to the nearest thousandth

 angle if the terminal side of an angle in standard position coincides with one of the axes.

A full rotation is represented by 360°.  Measures of more than that represent multiple rotations.  What would the degree measurement be for 5.5 rotations clockwise?  How about 3.3 rotations counterclockwise?  Based on your answers to those questions, develop a simple formula for an angle with a measurement of 

> 360° in either direction.  Can that equation be applied to an angle with a measurement < 360° ?

Any two angles in standard position that share a terminal side are called 

 angles.  Inventive, huh?  How does the derived formula above relate to coterminal angles?  Try identifying how to calculate all coterminal angles to 45°.  How about 225°?  Try to name at least one specific positive and negative example of  a coterminal to those two measurements.

For the different locations listed below, do some research to find the gps “address” of each exact location.   

 is a good resource - results are given in degrees.

What is the latitude measurement for the locations listed below?  What is one positive and one negative coterminal angle for each?  Convert the standard position angle into degrees, minutes, and seconds format.

Where in the World?