Explanation Definition used: Definition of the trigonometric functions : “Let ( x , y ) be any point on the terminal side of the angle θ in standard position, and let r be the distance between the origin and the given point, then the six trigonometry functions are defined as sin θ = y r , cos θ = x r , tan θ = y x , csc θ = r y , sec θ = r x and cot θ = x y ”. Theorem used: Pythagorean theorem: “If c is the length of the hypotenuse and a and b are the length of the other two sides, the Pythagorean theorem is c 2 = a 2 + b 2 ”. Calculation: The given functions are csc θ and cos θ and the points are ( 40 , 30 ) , ( 56 , 42 ) and ( 36 , 27 ) . Consider the point ( 40 , 30 ) to find the values of csc θ and cos θ . Let x = 40 and y = 30 and use the Pythagorean Theorem to find the value of r as follows. r = x 2 + y 2 = ( 40 ) 2 + ( 30 ) 2 = 1600 + 900 = 2500 = 50 The current situation can be represents as shown below in Figure 1. From Figure 1, it is observed that, the values of x = 40 , y = 30 and r = 50 . Find the values of the trigonometric functions csc θ and cos θ as follows. Substitute y = 30 and r = 50 in csc θ = r y , csc θ = 50 30 = 5 3 Substitute x = 40 and r = 50 in cos θ = x r , cos θ = 40 50 = 4 5 Therefore, the values of csc θ and cos θ are 5 3 and 4 5 _ , respectively. Consider the point ( 56 , 42 ) to find the values of csc θ and cos θ . Let x = 56 and y = 42 and use the Pythagorean Theorem to find the value of r as follows. r = x 2 + y 2 = ( 56 ) 2 + ( 42 ) 2 = 3136 + 1764 = 4900 = 70 The current situation can be represents as shown below in Figure 2

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 4.2, Problem 30E

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To show: The given function is same for each point.

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Chapter 4.2, Problem 29E

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Chapter 4 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

Ch. 4.1 - Change 17°24′ to decimal form. Ch. 4.1 - Prob. 2PE Ch. 4.1 - Prob. 3PE Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - Prob. 7E

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