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 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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