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 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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