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# Stereographic projections: A common way of displaying a ISBN: 9780321570567 2

## Solution for problem 46RE Chapter 1

Calculus: Early Transcendentals | 1st Edition

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Problem 46RE

Stereographic projections: A common way of displaying a sphere (such as Earth) on a plane (such as a map) is to use a ?stereographic proje ? ction. Here is the two-dimensional version of the method, which maps a circle to a line. Let ? P be a point on the right half of a circle of ra ? dius ? identified by the ?angle ??. Find the fu?nctio ? n?? = ? (? )that give? s the? -coordin ? ate (?x ? 0) corresponding to ? ?? fo? 0? ? ??.

Step-by-Step Solution:

Step-by-step solution Step 1 Given that P is a point on the right half of a circle of radius R identified by the angle as shown in the figure below, we need to find the function x = F() that gi es th -coordinate (x0) of the point P for 0 < . Step 2 To find F(), we disregard the circle and just consider the following part of the diagram: In the right triangle ACD, we know that: AB = BP = BC = R ABP = CD = x Looking at the figure, we see that AC constitutes the diameter of the circle with radius R , so: AC = 2R In triangle ABP , the sides AB and BP are equal that is: AB = BP Therefore, triangle ABP is an isosceles triangle.

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##### ISBN: 9780321570567

Since the solution to 46RE from 1 chapter was answered, more than 320 students have viewed the full step-by-step answer. The answer to “Stereographic projections: A common way of displaying a sphere (such as Earth) on a plane (such as a map) is to use a ?stereographic proje ? ction. Here is the two-dimensional version of the method, which maps a circle to a line. Let ? P be a point on the right half of a circle of ra ? dius ? identified by the ?angle ??. Find the fu?nctio ? n?? = ? (? )that give? s the? -coordin ? ate (?x ? 0) corresponding to ? ?? fo? 0<?? ? ??.” is broken down into a number of easy to follow steps, and 91 words. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The full step-by-step solution to problem: 46RE from chapter: 1 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This full solution covers the following key subjects: circle, such, stereographic, let, coordin. This expansive textbook survival guide covers 85 chapters, and 5218 solutions.

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