To determine To show: The given function is the same for each point. 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 cos θ and cot θ and the points are ( 5 , 12 ) , ( 15 , 36 ) and ( 7.5 , 18 ) . Consider the point ( 5 , 12 ) to find the values of cos θ and cot θ . Let x = 5 and y = 12 and use the Pythagorean Theorem to find the value of r as follows. r = x 2 + y 2 = 5 2 + 12 2 = 25 + 144 = 169 = 13 The current situation can be represents as shown below in Figure 1. From Figure 1 it is observed that, the values of x = 5 , y = 12 and r = 13 . Find the values of the trigonometric functions cos θ and cot θ as follows. Substitute x = 5 and r = 13 in cos θ = x r , cos θ = 5 13 Substitute x = 5 and y = 12 in cot θ = x y , cot θ = 5 12 Therefore, the values of cos θ and cot θ are 5 13 and 5 12 _ , respectively. Consider the point ( 15 , 36 ) to find the values of cos θ and cot θ . Let x = 15 and y = 36 and use the Pythagorean Theorem to find the value of r as follows. r = x 2 + y 2 = 15 2 + 36 2 = 225 + 1296 = 1521 = 39 The current situation can be represents as shown below in Figure 2

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

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ISBN: 9780137554843

Author: Allyn Washington, Richard Evans

Publisher: PEARSON+

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Chapter 4.2, Problem 28E

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

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Chapter 4.2, Problem 27E

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Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

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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