A geometry problem by George Gelyu Yguel Lucas

Geometry Level pending

About the numbers 3/2015 , π/2015 and sen(π/2015). What's the correct answer?

3/2015 < sen(π/2015) < π/2015 3/2015 < π/2015 < sen(π/2015) sen(π/2015) < 3/2015 < π/2015 3/2015 < π/2015 = sen(π/2015)

George Gelyu Yguel Lucas by George Gelyu Yguel Lucas , 22, Brazil

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1 solution

Caleb Townsend
Feb 10, 2015

Assuming he means sin ⁡ \sin rather than sen...
Note that d d x sin ⁡ x ≈ 1 − ϵ \frac{d}{dx} \sin x \approx 1 - \epsilon near x = 0 x = 0 , where ϵ \epsilon is a very small number. For that reason, sin ⁡ ( π / 2015 ) ≈ π / 2015 , \sin (\pi / 2015) \approx \pi / 2015, but also sin ⁡ ( π / 2015 ) < π / 2015. \sin (\pi / 2015) < \pi / 2015. We also know π > 3. \pi > 3. Therefore π 2015 > sin ⁡ π 2015 > 3 2015 \frac{\pi}{2015} > \sin\frac{\pi}{2015} > \frac{3}{2015}

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