trigonometry - Why $\sin(n\pi) = 0$ and $\cos(n\pi)=(-1)^n ...
$ => sin(n\pi) = \frac{exp(in\pi) - exp(-in\pi)}{2i}$ You can think of the positive exponential term as rotating counterclockwise, and the negative exponential term rotating clockwise. Since both …
trigonometry - Why is the sin of n times pi always 0 - Mathematics ...
Mar 22, 2016 · My instructor says that $\sin(\pi \cdot n)$ is always equal to $0$. However, when playing with jsconsole.com, I find that this is not the case. Math.sin(10000000000000000000 * …
How to write sin(n*pi/2) as an expression (-1)^f(n)? - Physics Forums
Feb 18, 2024 · I could summarize this as ##\frac{1}{n\pi}## for ##n=1, 5, 9, \ldots## ##\frac{-1}{n\pi}## for ##n=3, 7, 11, \ldots## and ##0## for all other ##n##.
sequences and series - Limit of $\sin(\pi n)$ as $n$ approaches ...
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How is sin(npi/2) = (-1)^((n-1)/2) for odd n? - Physics Forums
Sep 19, 2009 · sin(npi/2) is going to be equal to -1 or 1, depending on the value of n, right? So the formula seems plausible.
Simplifying Trigonometric Functions with Arbitrary n - Physics …
Feb 28, 2012 · ok i know that sin n*(pi/2) = 1 if n=1,5,9,13... = -1 if n=3,7,11,15... = 0 if n is even cos n*(pi/2) = 0 ...
real analysis - Limit of $sin(n\pi/2)$ as $n$ goes to $\infty ...
Apr 13, 2023 · Exercise 3.2, Question 16 from Introduction to Real Analysis by Bartle & Sherbert: Show that $\lim_{n \to \infty} \sin \frac{n\pi}{2}$ doesn't exist.
Prove $a_n = \\sin(n\\pi /2)$ does not converge to $0$
Apr 15, 2016 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …
How to explain that $\\sin(x) = 0$ gives $x = n\\pi$
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their …
trigonometry - Prove that the sequence $\sin\left (\frac {n\pi} {3 ...
I don't want to hear that since $\sin$ is a periodic function, etc, then we are done. I would like to see a simple proof that make use of the definition of convergence of a sequence. I have tried …