High School How to find out various sine values from its graph.

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The discussion focuses on identifying sine values from its graph, particularly addressing the behavior of the sine function at critical points. Participants agree that while most values are correctly identified, there is contention regarding the points pi/2 and 3pi/2, where the sine function neither increases nor decreases. The derivative at these points is noted to be a horizontal line, indicating a local maximum or minimum. Overall, the conversation emphasizes the importance of understanding the behavior of sine at specific intervals. Accurate interpretation of these points is crucial for analyzing the sine function effectively.
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Question (and Answer):

XtPLM.jpg

The answer is written in thin black, inc = increasing, dec = decreasing. Am I wrong anywhere?

Thanks!
 
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I would quibble over pi/2 and 3pi/2. In both of those cases the value of sin(x)neither increases nor decreases as x increases .
 
.Scott said:
I would quibble over pi/2 and 3pi/2. In both of those cases the value of sin(x)neither increases nor decreases as x increases .
Same here. Everything else is correct.
 
.Scott said:
I would quibble over pi/2 and 3pi/2. In both of those cases the value of sin(x)neither increases nor decreases as x increases .
Yeah, I also spent more time on those than others. I can see that the derivative there would be a horizontal straight line. Fine, thank you! :smile:
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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