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 37E
To determine

To determine: The simplified form of the expression using fundamental identities.

Expert Solution & Answer
Check Mark

Answer to Problem 37E

The required expression is secβ .

Explanation of Solution

Given information:

The trigonometric expression: sinβtanβ+cosβ

Formula used:

Trigonometric fundamental identities:

  tanx=sinxcosx

  sin2x+cos2x=1

  1cosx=secx

Calculation:

The given trigonometric expression is sinβtanβ+cosβ .

Rewrite the above expression using the formula tanx=sinxcosx as:

  sinβtanβ+cosβ=sinβsinβcosβ+cosβ=sin2β+cos2βcosβ

To simplify the above expression, use the formulas sin2x+cos2x=1 and 1cosx=secx .

  sin2β+cos2βcosβ=1cosβ=secβ

Hence, the required expression is secβ .

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Chapter 5.1, Problem 36E
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Chapter 5.1, Problem 38E

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