Let a be a real number. If cos a is rational, then cos(na) is rational for every positive integer n. 相关知识点: 试题来源: 解析 This result gives us a useful criterion for determining some irrational values of .More precisely,if we can show that,for a particular angle ,the value...
Since the maximum value of the cos in e function is 1, the maximum value of x+√1−x2 is √2, and equality is attained when θ=π4, i.e, when x=√22. 结果一 题目 If x is a real number and −1⩽x⩽1, find the maximum value of x+√1−x2若x是实数,且−1⩽...
What is the complex conjugate of a real number? Complex Conjugates: In mathematics, a complex number is a number of the forma+bi, whereaandbare real numbers andiis the imaginary number−1. We callathe real part of the number, and we callbithe imaginary part of the number. The complex...
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49,50 This is because observables of two single real qubits do not linearly generate all observables of two real qubits. In particular, if σy is the Pauli matrix with purely imaginary entries, then σy is not a real qubit observable, but σy ⊗ σy is a real two-qubit observable....
What are the "real numbers," really?The short, simple answer used in calculus courses is that a real number is a point on the number line. That's not the whole truth, but it is adequate for the needs of freshman calculus. The freshman calculus course (at most universities nowadays) ...
Find all real numbers {eq}a {/eq} such that the given point is on the circle {eq}\displaystyle x^2 + y^2 = 1 {/eq}. {eq}\left (-\dfrac 7 8,\ a\right ) {/eq} Circle: definition and standard form equation: Circle: In Geometry, a circle is def...
Consider the polynomial (x - a)(x - b) and the real number line (see figure). Identify the points on the line where the polynomial is zero. Graph an equation for values of x between 0 degree and 360 degrees on multiples of 15 degrees. y = 6cos(x). ...
Let's go for a more advanced example where we calculate the fixpoint of the cosine function, i.e. the value where cos(x) == x.Implementations in imperative languages usually involve introducing local mutable state. Not so in Frege:
Fast polynomial lookup table-based floating-point approximations for cos, log2, exp2, pow and others. Original math functions such as a short Gaussian function and its integral, the short error function which I now use for filter design. I also implemented the inverse of the error function an...