2015年5月30日 · We know that cos(2π/n) = (e2πi/n +e−2πi/n)/2 and both e2πi/n and e−2πi/n are complex numbers which are roots of xn − 1, so these are algebraic integers.

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For an integer , the minimal polynomial of is the non-zero monic polynomial of smallest degree for which . For every n, the polynomial is monic, has integer coefficients, and is irreducible over the integers and the rational numbers.

2019年9月14日 · If cos(2π n) cos (2 π n) is rational, any σ ∈ Gal(Q(ζ)/Q) σ ∈ G a l (Q (ζ) / Q) must fix it. Since ζ ζ is a root of the polynomial tn − 1 ∈Q[t] t n − 1 ∈ Q [t], so is σ(ζ) σ (ζ).

If pi, 1 ≤ i ≤ n p i, 1 ≤ i ≤ n on unit circle forms a regular n n -gon, then define R R to be 2π n 2 π n -rotation. Hence p1 + ⋯ +pn p 1 + ⋯ + p n is invariant under R R so that it is 0 0 -vector.

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Cos 2pi gives the value of the cosine function when the angle made with the positive x-axis is 2pi, that is, one complete rotation. We study values of trigonometric functions at some standard angles like 0, π/6, π/4, π/3/ π/2 (in radians) and use them to solve various problems to determine the trigonometric values with non-standard angles.

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2025年3月22日 · 一、引言 高考的比大小题目中，除了 e^x 和 \ln {x} ，出现较多的就是 \sin {x},\cos {x},\tan {x} 这几个三角函数。导数大题中，也有可能出现这些函数。因此，我们需要研究这几个函数的性质，其中， x\in (0,\frac {\pi} {2}) 是研究这几个函数性质的重要区间。根据三角函数的周期性和对称性，其他区间上的 ...