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

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The functions cos(pi + x) and -cos(x) are mathematically equivalent, yet their graphs exhibit distinct characteristics due to the phase shift introduced by the pi term. While both functions yield the same output for any given x, the graph of cos(pi + x) is a horizontal shift of -cos(x) by pi units. This difference in graph appearance stems from the periodic nature of the cosine function, which repeats every 2*pi. Despite the visual differences, the underlying values remain consistent across both functions. Understanding this concept highlights the nuances of trigonometric functions and their graphical representations.
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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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