Question regarding Cosine Function

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    Cosine Function
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The cosine function represents the ratio of the adjacent side to the hypotenuse in a right-angled triangle. Its properties can be visualized through graphing, which reveals its well-known characteristics. The relationship between the cosine function and squares indicates that the square of any function is always non-negative. Understanding these properties clarifies the application of the cosine function in various mathematical contexts. This foundational knowledge is essential for effectively utilizing the cosine function.
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Do anyone know what properties of cosine function should we use? and the method to use it? kinda blur...
 

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The cosine is the ratio of the adjacent side of a right-angled triangle to it's hypotenuse.
If you sketch a graph of the cosine function, you see it obeys the first relation ... that's the "well known properties" that they are talking about. The second relation actually follows from the properties of a square (the power of two).

Sketch them and you'll see.
 
Thanks...I finally got it. Square of any function must be greater or equal to 0...
 
Well done :)
 

Thread 'Area of Overlapping Squares'

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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