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 sin θ and tan θ and the points are ( 3 , 4 ) , ( 6 , 8 ) and ( 4.5 , 6 ) . Consider the point ( 3 , 4 ) to find the values of sin θ and tan θ . Let x = 3 and y = 4 and use the Pythagorean Theorem to find the value of r as follows. r = x 2 + y 2 = 3 2 + 4 2 = 9 + 16 = 25 = 5 The current situation can be represents as shown below in Figure 1. From Figure 1 it is observed that, the values of x = 3 , y = 4 and r = 5 . Find the values of the trigonometric functions sin θ and tan θ as follows. Substitute r = 5 and y = 4 in sin θ = y r , sin θ = 4 5 Substitute x = 3 and y = 4 in tan θ = y x , tan θ = 4 3 Therefore, the values of sin θ and tan θ are 4 5 and 4 3 _ , respectively. Consider the point ( 6 , 8 ) to find the values of sin θ and tan θ . Let x = 6 and y = 8 and use the Pythagorean Theorem to find the value of r as follows. r = x 2 + y 2 = 6 2 + 8 2 = 36 + 64 = 100 = 10 The current situation can be represents as shown below in Figure 2

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ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 4.2, Problem 27E

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

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Chapter 4.2, Problem 26E

Chapter 4.2, Problem 28E

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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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