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(a) If(tanh x) = 1/4, find the value of sinh x without a calculator. Show the procedure of your solution.

(a) If(tanh x) = 1/4, find the value of sinh x without a calculator. Show the procedure of your solution.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.3: Trigonometric Functions Of Real Numbers
Problem 43E
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Question 5 (a) If — (tanh x) = 1/4, find the value of sinh x without a calculator. Show the dx procedure of your solution. У 4 s(x, y) (b) a Figure 5.1 The graph of a catenary in the Cartesian coordinates is shown in Figure 5.1. The two poles, A and B, have the same height to the x-axis, and the same distance to the y-axis. For a given point on the catenary, s(x, y), we have, y = acosh(). (1) It is also known that the length of the catenary segment between C (the lowest point of the catenary) and point s, i.e., Is, is given by, y²-1²=a². (2) If the total length of the catenary between A and B, i.e., LAB, is 20 m and a is 10 m, determine (i) the height of the pole, i.e. H, as shown in the figure. (ii) the distance between A and B, i.e., D, as shown in the figure. LAB H D 1₂
Transcribed Image Text:Question 5 (a) If — (tanh x) = 1/4, find the value of sinh x without a calculator. Show the dx procedure of your solution. У 4 s(x, y) (b) a Figure 5.1 The graph of a catenary in the Cartesian coordinates is shown in Figure 5.1. The two poles, A and B, have the same height to the x-axis, and the same distance to the y-axis. For a given point on the catenary, s(x, y), we have, y = acosh(). (1) It is also known that the length of the catenary segment between C (the lowest point of the catenary) and point s, i.e., Is, is given by, y²-1²=a². (2) If the total length of the catenary between A and B, i.e., LAB, is 20 m and a is 10 m, determine (i) the height of the pole, i.e. H, as shown in the figure. (ii) the distance between A and B, i.e., D, as shown in the figure. LAB H D 1₂
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