Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music…

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.

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.

Sep 14, 2019 · We know $\cos(2\pi)=1$ and $\cos(\pi)=-1$. Let $n \geq 3 $ be a positive integer and $\zeta = e^{\frac{2\pi i}{n}}$ be the first root of unity. Assume …

To solve a trigonometric simplify the equation using trigonometric identities. Then, write the equation in a standard form, and isolate the variable using algebraic manipulation to solve for …

May 30, 2015 · We know that $\cos(2\pi/n)=(e^{2\pi i/n}+e^{-2\pi i /n})/2$ and both $e^{2\pi i/n}$ and $e^{-2\pi i/n}$ are complex numbers which are roots of $x^n-1$, so these are algebraic integers.

The exact value of cos(0) cos (0) is 1 1. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.

Dec 8, 2016 · First, you can say cos 2 (x)=1/4 so cos (x)=1/2 or cos (x)=-1/2. Then you get FOUR solutions, two from each case: x=pi/3 +2pi (n), x=2pi/3+2pi (n), x=4pi/3+2pi (n), x=5pi/3+2pi (n). Second, you can use a double-angle identity to replace cos 2 (x) with [1+cos (2x)]/2.

Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music…

Enter a problem... Reorder factors in cos(2)π cos (2) π. The result can be shown in multiple forms. −1.30736384… - 1.30736384 … Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.