Comparing Trigonometric and Fractional Values: Which is Greater?

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Discussion Overview

The discussion revolves around comparing the values of the expression $\sin 1 - \cos 1$ and the fraction $\frac{1}{4}$. Participants explore the numerical relationship between these two quantities, considering both direct calculation and mathematical expansion methods.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions which is greater between $\sin 1 - \cos 1$ and $\frac{1}{4}$.
  • Another participant suggests that $\sin 1 - \cos 1$ is the answer, but does not provide justification.
  • A request for a numerical evaluation of $\sin(1) - \cos(1)$ is made, indicating a desire for empirical evidence.
  • One participant mentions using expansion methods to approach the problem, implying a mathematical technique without detailing it.
  • There is a reiteration of the answer being $\sin 1 - \cos 1$, but it is unclear if this is agreed upon by all participants.

Areas of Agreement / Disagreement

Participants do not reach a consensus on which value is greater, and multiple viewpoints regarding the evaluation methods and answers remain present.

Contextual Notes

Some assumptions about the values of $\sin(1)$ and $\cos(1)$ are not explicitly stated, and the discussion lacks detailed mathematical steps for the expansion method mentioned.

anemone
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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)
 

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