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 tan θ and sec θ and the points are ( 0.3 , 0.1 ) , ( 9 , 3 ) and ( 33 , 11 ) . Consider the point ( 0.3 , 0.1 ) to find the values of tan θ and sec θ . Let x = 0.3 and y = 0.1 and use the Pythagorean Theorem to find the value of r as follows. r = x 2 + y 2 = ( 0.3 ) 2 + ( 0.1 ) 2 = 0 .09 + 0.01 = 0.1 The current situation can be represents as shown below in Figure 1. From Figure 1 it is observed that, the values of x = 0.3 , y = 0.1 and r = 0.1 . Find the values of the trigonometric functions tan θ and sec θ as follows. Substitute x = 0.3 and y = 0.1 in tan θ = y x . tan θ = 0.1 0.3 = 1 3 Substitute x = 0.3 and r = 0.1 in sec θ = r x . sec θ = 0.1 0.3 = 10 3 Therefore, the values of tan θ and sec θ are 1 3 and 10 3 _ respectively. Consider the point ( 9 , 3 ) to find the values of tan θ and sec θ . Let x = 9 and y = 3 and use the Pythagorean theorem to find the value of r as follows. r = x 2 + y 2 = 9 2 + 3 2 = 81 + 9 = 90 = 3 10 The current situation can be represents as shown below in Figure 2

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 4.2, Problem 29E

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

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Chapter 4 Solutions

Basic Technical Mathematics

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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