MHB Comparing Trigonometric and Fractional Values: Which is Greater?

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The discussion revolves around comparing the values of $\sin 1 - \cos 1$ and $\frac{1}{4}$. Participants express uncertainty about the calculation and the method used to determine which value is greater. There is an emphasis on providing not just the final answer but also the solving method for clarity. The conversation highlights the importance of engaging with the problem-solving process in mathematical discussions. Ultimately, the focus remains on evaluating the comparison between the two expressions.
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Which number is bigger, $\sin 1-\cos 1$ or $\dfrac{1}{4}$?
 
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Is the answer $sin1 - cos1$
 
What does a calculator give for sin(1)- cos(1)?
 
I don't know I just used expansion for this.
 
DaalChawal said:
Is the answer $sin1 - cos1$
Yeap!(Cool) For your information, a challenge problem posted in this sub forum is meant for the interested members to post not only the final answer, but also the method of solving as well. (Nod)
 

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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