Solving Problems with Graphs: Step-by-Step Guide

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The discussion focuses on solving problems involving graphs of sine functions, specifically determining the constants c, d, and k in given equations. The user seeks a step-by-step explanation rather than just answers to enhance understanding. For the first problem, it is suggested to explore different values of c in relation to 10, while for the second problem, varying d around 12 and considering integer values for k is recommended. The importance of understanding the general behavior of the functions through these constants is emphasized. Overall, the conversation aims to clarify the process of analyzing and graphing trigonometric functions.
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Problem with graphs

Hi!
I hope this is the right place to post this.

I'm having problem with this kind of problems. I hope you could explain step by step on how you're solving this. To be sure that I understand well I'm posting two examples. Both of them are from old math tests I'm reding to prepare myself for my test.

1:
y = 10sinx + csin2x
What's c?

http://home.tiscali.se/21355861/bilder/graph1.PNG

...

2:
y = 12sinx
y = 12sinx + dsinkx

What's d and k?

http://home.tiscali.se/21355861/bilder/graph2.PNG


I hope someone can explain this. Please don't just give me the answer because I want to understand it.

Thank you in advance
:smile:

Edit: it should be graphs not graphes :blushing:
 
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In both cases the letters you are asking about represent constants. However, particular values for these constants have not been supplied. To graph the functions, you would need them. However some general properties can be seen by trying a few cases. In problem 1, try c>10, c=10, c<10, also negative values of the same magnitude. For problem 2, similarly for d (using 12 as the break point). I assume k is supposed to be an integer, so try different values, noting that k=2 is basically problem 1.
 
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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