Precalculus with Limits: A Graphing Approach
Precalculus with Limits: A Graphing Approach
7th Edition
ISBN: 9781305071711
Author: Ron Larson
Publisher: Brooks/Cole
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Concept explainers

Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
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Question
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Chapter 5.2, Problem 66E
To determine

To verify the identity:

  ln|secθ|=−ln|cosθ|

Expert Solution & Answer
Check Mark

Explanation of Solution

Given:

  ln|secθ|=−ln|cosθ|

Concept Used:

  • The trigonometric identity: secx=1cosx
  • Power property of logarithmic function: lnun=nlnu

Calculation:

In order to verify the identity:

  ln|secθ|=−ln|cosθ|

Take left hand of above identity and simplify it using the trigonometric identity and logarithmic property.

As,

  ln|secθ|=ln|1cosθ|=ln|(cosθ)−1|=−ln|cosθ|; Power property=Right hand

Thus, identity is verified, i.e.

  ln|secθ|=−ln|cosθ|

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Chapter 5.2, Problem 65E
Next
Chapter 5.2, Problem 67E

Chapter 5 Solutions

Precalculus with Limits: A Graphing Approach

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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