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3. A map projection is a set of equations used to visualize the surface of the earth on a two-dimensional map. The act of displaying a curved surface on a flat surface will always result in some sort of stretching, splitting or distortion. Think about the challenges of flattening an orange peel! The Mercator projection, proposed in 1569, is a very famous map projection. It was very popular because of how useful it is as a navigational chart. Any straight line on a Mercator map corresponds to a straight-line course - it makes it easy to cross an ocean. The big problem with the Mercator projection is that scale is highly distorted. On a Mercator map, areas far from the equator appear far larger than they actually are. Have a look at the map below. It looks like Greenland is larger than Africa, but Africa is actually 14 times larger. In this question, we'll look at the math behind the Mercator projection. In this projection, A, ø will represent the longitude and latitude, respectively, of a point on the Earth's surface and (r, y) will represent the location of that same point on the map, where we will place the r-axis along the Equator and the y-axis along the Prime Meridian. If R is a positive scaling constant, then the y-coordinate on the map of a location with latitude ø is given by y = Rln ( tan (a) Evaluate lim y to explain what happens as you try to map a point near the North Pole. (b) Evaluate 4. Express your answer entirely in terms of the secant and cosecant functions.

3. A map projection is a set of equations used to visualize the surface of the earth on a two-dimensional map. The act of displaying a curved surface on a flat surface will always result in some sort of stretching, splitting or distortion. Think about the challenges of flattening an orange peel! The Mercator projection, proposed in 1569, is a very famous map projection. It was very popular because of how useful it is as a navigational chart. Any straight line on a Mercator map corresponds to a straight-line course - it makes it easy to cross an ocean. The big problem with the Mercator projection is that scale is highly distorted. On a Mercator map, areas far from the equator appear far larger than they actually are. Have a look at the map below. It looks like Greenland is larger than Africa, but Africa is actually 14 times larger. In this question, we'll look at the math behind the Mercator projection. In this projection, A, ø will represent the longitude and latitude, respectively, of a point on the Earth's surface and (r, y) will represent the location of that same point on the map, where we will place the r-axis along the Equator and the y-axis along the Prime Meridian. If R is a positive scaling constant, then the y-coordinate on the map of a location with latitude ø is given by y = Rln ( tan (a) Evaluate lim y to explain what happens as you try to map a point near the North Pole. (b) Evaluate 4. Express your answer entirely in terms of the secant and cosecant functions.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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3. A map projection is a set of equations used to visualize the surface of the earth on a two-dimensional map. The act of displaying a curved surface on a flat surface will always result in some sort of stretching, splitting or distortion. Think about the challenges of flattening an orange peel! The Mercator projection, proposed in 1569, is a very famous map projection. It was very popular because of how useful it is as a navigational chart. Any straight line on a Mercator map corresponds to a straight-line course - it makes it easy to cross an осean. The big problem with the Mercator projection is that scale is highly distorted. On a Mercator map, areas far from the equator appear far larger than they actually are. Have a look at the map below. It looks like Greenland is larger than Africa, but Africa is actually 14 times larger. In this question, we'll look at the math behind the Mercator projection. In this projection, A, ø will represent the longitude and latitude, respectively, of a point on the Earth's surface and (r, y) will represent the location of that same point on the map, where we will place the r-axis along the Equator and the y-axis along the Prime Meridian. If R is a positive scaling constant, then the y-coordinate on the map of a location with latitude o is given by y = Rln ( tan (a) Evaluate lim y to explain what happens as you try to map a point near the North Pole. (b) cosecant functions. Evaluate . Express your answer entirely in terms of the secant and (c) Solve the above equation for Q to give a formula that you could use to find the latitude of a location if you knew it's location on a map, that is, if you knew it's y-coordinate on the map.
Transcribed Image Text:3. A map projection is a set of equations used to visualize the surface of the earth on a two-dimensional map. The act of displaying a curved surface on a flat surface will always result in some sort of stretching, splitting or distortion. Think about the challenges of flattening an orange peel! The Mercator projection, proposed in 1569, is a very famous map projection. It was very popular because of how useful it is as a navigational chart. Any straight line on a Mercator map corresponds to a straight-line course - it makes it easy to cross an осean. The big problem with the Mercator projection is that scale is highly distorted. On a Mercator map, areas far from the equator appear far larger than they actually are. Have a look at the map below. It looks like Greenland is larger than Africa, but Africa is actually 14 times larger. In this question, we'll look at the math behind the Mercator projection. In this projection, A, ø will represent the longitude and latitude, respectively, of a point on the Earth's surface and (r, y) will represent the location of that same point on the map, where we will place the r-axis along the Equator and the y-axis along the Prime Meridian. If R is a positive scaling constant, then the y-coordinate on the map of a location with latitude o is given by y = Rln ( tan (a) Evaluate lim y to explain what happens as you try to map a point near the North Pole. (b) cosecant functions. Evaluate . Express your answer entirely in terms of the secant and (c) Solve the above equation for Q to give a formula that you could use to find the latitude of a location if you knew it's location on a map, that is, if you knew it's y-coordinate on the map.
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