Comparing Trigonometric and Fractional Values: Which is Greater?

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SUMMARY

The discussion centers on comparing the values of $\sin(1) - \cos(1)$ and $\frac{1}{4}$. Participants confirm that the expression $\sin(1) - \cos(1)$ is indeed the focus of the comparison. Calculators can be used to evaluate this expression, but the discussion emphasizes the importance of providing both the final answer and the method of solving the problem. The consensus is that $\sin(1) - \cos(1)$ is the correct approach to determine which value is greater.

PREREQUISITES
  • Understanding of trigonometric functions, specifically sine and cosine.
  • Familiarity with numerical evaluation of trigonometric expressions.
  • Basic knowledge of mathematical inequalities.
  • Ability to perform Taylor series expansions for trigonometric functions.
NEXT STEPS
  • Learn how to evaluate trigonometric functions using calculators or software tools.
  • Research Taylor series expansions for $\sin(x)$ and $\cos(x)$.
  • Explore methods for comparing real numbers and inequalities in calculus.
  • Investigate the properties of trigonometric functions in the context of their ranges and behaviors.
USEFUL FOR

Students, mathematicians, and anyone interested in trigonometry or solving mathematical inequalities will benefit from this discussion.

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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