To determine The all values of θ between 0 and 2 π that satisfies the equation sec θ = 2 . Explanation Properties of a right triangle Triangle with 30 ° − 60 ° − 90 ° : “In a right triangle having angles of 30 ° , 60 ° , and 90 ° the hypotenuse is always twice as long as the shortest side, and the middle side has a length that is 3 times as long as that of the shortest side. Also, the shortest side is opposite the 30 ° angle. Triangle with 45 ° − 45 ° − 90 ° : In a right triangle having angles of 45 ° , 45 ° , and 90 ° the hypotenuse has a length that is 2 times as long as the length of either of the shorter (equal ) sides.” Formula used: “Let ( x , y ) be a point other than the origin on the terminal side of an angle θ in standard position. Let r be the distance from the origin to ( x , y ) . Then sin θ = y r , cos θ = x r , tan θ = y x , cot θ = x y , sec θ = r x and csc θ = r y ”. Pythagorean theorem: In a triangle with a right angle, if the longest side of the triangle c and the shorter sides are a and b , then c 2 = a 2 + b 2 . Here, longest side of the triangle is r and shorter sides are x and y . Calculation: Consider the equation sec θ = 2 . By the above formula, sec θ can be defined as sec θ = r x . That is, r = 2 and x = 1 . In order to find the all values of θ between 0 and 2 π , first find value of y

Calculus with Applications (11th Edition)

11th Edition

ISBN: 9780321979421

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 13.1, Problem 54E

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The all values of θ between 0 and 2π that satisfies the equation secθ=2.

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Chapter 13.1, Problem 53E

Chapter 13.1, Problem 55E

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Chapter 13 Solutions

Calculus with Applications (11th Edition)

Ch. 13.1 - (a) Convert 210° to radians. (b) Convert 3π/4...Ch. 13.1 - Find the values of the six trigonometric functions...Ch. 13.1 - Prob. 3YT Ch. 13.1 - Prob. 4YT Ch. 13.1 - Find all values of θ between 0 and 2π that satisfy...Ch. 13.1 - Convert the following degree measures to radians....Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Convert the following degree measures to radians....Ch. 13.1 - Prob. 5E

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