Understanding the Difference Between cos(pi +x) and -cos(x)

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Discussion Overview

The discussion revolves around the functions cos(pi + x) and -cos(x), focusing on their equivalence and the differences in their graphical representations. Participants explore the implications of these differences in the context of trigonometric properties and cyclic behavior.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • One participant asserts that cos(pi + x) and -cos(x) are the same but notes that their graphs appear different.
  • Another participant questions how the graphs can differ if the functions are equivalent.
  • A third participant mentions the cyclic nature of the cosine function, suggesting that periodicity may play a role in understanding the behavior of these functions.

Areas of Agreement / Disagreement

Participants express confusion regarding the relationship between the functions and their graphical representations, indicating that there is no consensus on the nature of their equivalence and differences.

Contextual Notes

The discussion does not clarify the specific characteristics of the graphs that lead to the perceived differences, nor does it resolve the implications of the cyclic nature of the cosine function on this topic.

aznluster
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The two functions cos(pi +x) and -cos(x) are the same yet their graphs are different. Why is that?
 
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How are their graphs different?
 
And if there graphs were different, how could the two functions be the same?
 
Cosine is cyclic. Every 2*pi revolutions of a unit vector brings the value back to the same value.
 

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