7th Edition

ISBN: 9780100548169

Author: SMITH

Publisher: YUZU

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.

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Textbook Question

Chapter 64, Problem 80A

Determine the value of angle A in decimal degrees for each of the given functions. Round the answers to the nearest hundredth of a degree.
cos A = 0.20893

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Chapter 64, Problem 79A

Chapter 64, Problem 81A

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Use the Euclidean algorithm to find two sets of integers (a, b, c) such that 55a65b+143c: Solution = 1. By the Euclidean algorithm, we have: 143 = 2.65 + 13 and 65 = 5.13, so 13 = 143 – 2.65. - Also, 55 = 4.13+3, 13 = 4.3 + 1 and 3 = 3.1, so 1 = 13 — 4.3 = 13 — 4(55 – 4.13) = 17.13 – 4.55. Combining these, we have: 1 = 17(143 – 2.65) - 4.55 = −4.55 - 34.65 + 17.143, so we can take a = − −4, b = −34, c = 17. By carrying out the division algorithm in other ways, we obtain different solutions, such as 19.55 23.65 +7.143, so a = = 9, b -23, c = 7. = = how ? come [Note that 13.55 + 11.65 - 10.143 0, so we can obtain new solutions by adding multiples of this equation, or similar equations.]

- Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p − 1)/2 multiple of n, i.e. n mod p, 2n mod p, ..., p-1 2 -n mod p. Let T be the subset of S consisting of those residues which exceed p/2. Find the set T, and hence compute the Legendre symbol (7|23). 23 32 how come? The first 11 multiples of 7 reduced mod 23 are 7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8. The set T is the subset of these residues exceeding So T = {12, 14, 17, 19, 21}. By Gauss' lemma (Apostol Theorem 9.6), (7|23) = (−1)|T| = (−1)5 = −1.

Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p-1)/2 multiple of n, i.e. n mod p, 2n mod p, ..., 2 p-1 -n mod p. Let T be the subset of S consisting of those residues which exceed p/2. Find the set T, and hence compute the Legendre symbol (7|23). The first 11 multiples of 7 reduced mod 23 are 7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8. 23 The set T is the subset of these residues exceeding 2° So T = {12, 14, 17, 19, 21}. By Gauss' lemma (Apostol Theorem 9.6), (7|23) = (−1)|T| = (−1)5 = −1. how come?

Chapter 64 Solutions

EBK MATHEMATICS FOR MACHINE TECHNOLOGY

Ch. 64 - Prob. 1A Ch. 64 - Prob. 2A Ch. 64 - The steel beam shown weighs 7800 kilograms/cubic...Ch. 64 - A triangle has a base of 8.4 cm and a height of...Ch. 64 - Determine the diameter of a circle with a...Ch. 64 - Use a protractor to measure this angle. If...Ch. 64 - With reference to 1, name each of the sides of the...Ch. 64 - With reference to 1, name each of the sides of the...Ch. 64 - With reference to 1, name each of the sides of the...Ch. 64 - With reference to 1, name each of the sides of the...

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Determine the value of angle A in decimal degrees for each of the given functions. Round the answers to the nearest hundredth of a degree. cos A = 0.20893

Solution Summary: The author explains the value of angle A in decimal degree, which is 77.94°.

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