Explanation Formula used: Trigonometry ratios: sin θ = Opposite Hypotenuse , csc θ = Hypotenuse Opposite , cos θ = Adjacent Hypotenuse , sec θ = Hypotenuse Adjacent tan θ = Opposite Adjacent and cot θ = Adjacent Opposite . Theorem used: Pythagoras theorem: For a right triangle ABC , ( hypotenuse ) 2 = ( base ) 2 + ( opposite side ) 2 . Calculation: Consider a right triangle ACB with an angle 45 ° . The right triangle is as shown below in Figure 1. From Figure 1, it is observed that the adjacent and opposite side of the angle 45 ° is 1. Use Pythagoras theorem to obtain the hypotenuse of angle 45 ° as follows

Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

14th Edition

ISBN: 9780134668574

Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker

Publisher: PEARSON

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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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Chapter 8.1, Problem 20E

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To find: The exact value of csc45° without the use of a calculator.

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Chapter 8.1, Problem 19E

Chapter 8.1, Problem 21E

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Chapter 8 Solutions

Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

Ch. 8.1 - Find the degree measure of 1 rad.Ch. 8.1 - Without using a calculator, find: (A)cot 45 (B)cos...Ch. 8.1 - Solve the right triangle in Figure 14. Round side...Ch. 8.1 - Solve the right triangle in Figure 16. Round...Ch. 8.1 - Repeat Example 5 assuming that the man is standing...Ch. 8.1 - Prob. 1ED Ch. 8.1 - Prob. 1E Ch. 8.1 - In Problems 18, mentally convert each degree...Ch. 8.1 - In Problems 18, mentally convert each degree...Ch. 8.1 - In Problems 18, mentally convert each degree...

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The exact value of csc 45 ° without the use of a calculator.

Solution Summary: The author calculates the exact value of the trigonometric ratio mathrmcsc45° without the use of a calculator.

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