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 15E
To determine

To calculate: The values of all six trigonometric functions.

Expert Solution & Answer
Check Mark

Answer to Problem 15E

The required values of sinϕ , cosϕ , cotϕ and cscϕ are 817 , −1517 , −158 and 178 respectively.

Explanation of Solution

Given information:

The functions: secϕ=−1715 , tanϕ=−815

Formula used:

Trigonometric identities:

  sinϕ=1cscϕ

  secϕ=1cosϕ

  tanϕ=sinϕcosϕ

  cotϕ=1tanϕ

  sin2ϕ+cos2ϕ=1

  sec2ϕ=1+tan2ϕ

Calculation:

The given function is secϕ=−1715 , tanϕ=−815 .

So, cosϕ=1secϕ=1−1715=−1517

Use the formula tanϕ=sinϕcosϕ to find the value of sinϕ .

  sinϕ=tanϕcosϕ=(−815)(−1517)=817

  cscϕ=1sinϕ=1817=178

Also, cotϕ=1tanϕ=1−815=−158

Hence, the required values of sinϕ , cosϕ , cotϕ and cscϕ are 817 , −1517 , −158 and 178 respectively.

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Chapter 5.1, Problem 14E
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Chapter 5.1, Problem 16E

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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Prob. 34ECh. 5.4 - Prob. 35ECh. 5.4 - Prob. 36ECh. 5.4 - Prob. 37ECh. 5.4 - Prob. 38ECh. 5.4 - Prob. 39ECh. 5.4 - Prob. 40ECh. 5.4 - Prob. 41ECh. 5.4 - Prob. 42ECh. 5.4 - Prob. 43ECh. 5.4 - Prob. 44ECh. 5.4 - Prob. 45ECh. 5.4 - Prob. 46ECh. 5.4 - Prob. 47ECh. 5.4 - Prob. 48ECh. 5.4 - Prob. 49ECh. 5.4 - Prob. 50ECh. 5.4 - Prob. 51ECh. 5.4 - Prob. 52ECh. 5.4 - Prob. 53ECh. 5.4 - Prob. 54ECh. 5.4 - Prob. 55ECh. 5.4 - Prob. 56ECh. 5.4 - Prob. 57ECh. 5.4 - Prob. 58ECh. 5.4 - Prob. 59ECh. 5.4 - Prob. 60ECh. 5.4 - Prob. 61ECh. 5.4 - Prob. 62ECh. 5.4 - Prob. 63ECh. 5.4 - Prob. 64ECh. 5.4 - Prob. 65ECh. 5.4 - Prob. 66ECh. 5.4 - Prob. 67ECh. 5.4 - Prob. 68ECh. 5.4 - Prob. 69ECh. 5.4 - Prob. 70ECh. 5.4 - Prob. 71ECh. 5.4 - Prob. 72ECh. 5.4 - Prob. 73ECh. 5.4 - Prob. 74ECh. 5.4 - Prob. 75ECh. 5.4 - Prob. 76ECh. 5.4 - Prob. 77ECh. 5.4 - Prob. 78ECh. 5.4 - Prob. 79ECh. 5.4 - Prob. 80ECh. 5.4 - Prob. 81ECh. 5.4 - Prob. 82ECh. 5.4 - Prob. 83ECh. 5.4 - Prob. 84ECh. 5.4 - Prob. 85ECh. 5.4 - Prob. 86ECh. 5.4 - 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Inverse Trigonometric Functions; Author: Professor Dave Explains;https://www.youtube.com/watch?v=YXWKpgmLgHk;License: Standard YouTube License, CC-BY