Wikipedia:Reference desk/Archives/Mathematics/2016 July 24

= July 24 =

Sine Function
Hi, is that true that $$\alpha\cdot\sin(\beta x)$$ is $$\frac{2\pi}{\beta}$$-periodic (for every $$\alpha$$)? 31.154.81.45 (talk) 05:57, 24 July 2016 (UTC)


 * Yes. The constant factor &alpha; makes no difference to the periodicity. —Tamfang (talk) 06:28, 24 July 2016 (UTC)
 * Thank you! 80.246.138.78 (talk) 09:07, 24 July 2016 (UTC)

Order of Growth
What is the order of growth (=big-O notation, or Theta-notation), of $$e^{i\theta}$$ as $$\theta$$ tends to zero? 185.32.179.12 (talk) 12:05, 24 July 2016 (UTC)
 * O(1). In fact, $$\lim_{\theta\to 0} e^{i\theta}=1$$.   Sławomir Biały  (talk) 12:22, 24 July 2016 (UTC)
 * Thanks :) 31.154.81.45 (talk) 10:16, 25 July 2016 (UTC)


 * Would it help to mention that $$e^{i\theta} \approx 1+i\theta$$ in that neighborhood? —Tamfang (talk) 06:38, 26 July 2016 (UTC)