6. In this problem, we will assume the earth is perfectly spherical (which is not quite true), with a radius RE = 3959 mi. We measure a position on the earth using latitude and longitude . In degrees, these are defined by the following slight variation of ordinary spherical coordinates. Let X = (-90,90) (-180, 180) CR. Define : X R by $(0,0) = (REC cos TO 180 COS 180 RECOS TO 180 sin 180 , RE sin TO 180 (The factors of 180 are because o and 0 are to be measured in degrees.) Negative degrees latitude are considered south, while positive are considered north; similarly, negative degrees longitude are considered west, while positive are east. (a) The coordinates of Dallas on the longitude-latitude map are (32.8, -96.8). Sup- pose you start at this point and start heading due east at one degree longitude per hour. What is your speed in miles per hour? (b) What if you start at the same point, but start off heading north at one degree latitude per hour? (c) Now suppose that you are in the outskirts of Quito, Ecuador, at the point (0,-78.5) (on the equator). If you start heading due east at one degree longitude per hour, what is your speed in miles per hour? (d) What about if you head north from Quito at one degree latitude per hour? You may use calculators to evaluate numerical and trig expressions in this problem, but not for any calculus.