PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
8th Edition
ISBN: 9781337904285
Author: Larson
Publisher: CENGAGE L
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Trigonometric Identities
Trigonometry in mathematics deals with the right-angled triangle’s angles and sides. By trigonometric identities, we mean the identities we use whenever we need to express the various trigonometric functions in terms of an equation.
Inverse Trigonometric Functions
Inverse trigonometric functions are the inverse of normal trigonometric functions. Alternatively denoted as cyclometric or arcus functions, these inverse trigonometric functions exist to counter the basic trigonometric functions, such as sine (sin), cosi…
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Question
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Chapter 5.1, Problem 5E
To determine

To fill in the blank to complete the trigonometric identity sec(−u)=____ .

Expert Solution & Answer
Check Mark

Answer to Problem 5E

  secu

Explanation of Solution

Given:

The expressions, sec(−u)=____

Concept Used:

Out of six trigonometric functions, only cosine and secant are even function. All other four trigonometric functions are odd.

Calculation:

In order tofind the equivalent expression for the given trigonometric identity sec(−u) , use the fact that only cosine and secant functions are even functions.

By the definition of an even function, we know that for any function f(x) , the condition is f(−x)=f(x) .

Since, the given function is a secant function, so it is even as well and hence

  sec(−u)=secu

Thus, the complete trigonometric identity is sec(−u)=secu .

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Chapter 5.1, Problem 4E
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Chapter 5.1, Problem 6E

Chapter 5 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

Ch. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Prob. 7ECh. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Prob. 10E
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Inverse Trigonometric Functions; Author: Professor Dave Explains;https://www.youtube.com/watch?v=YXWKpgmLgHk;License: Standard YouTube License, CC-BY