1
$\begingroup$

Rewrite the function $2 + 4\sin(\pi t + \frac{\pi}{6})$ into a sum of exponential functions. By that I mean using Euler's formula $\sin(x) = \dfrac{e^{i\pi x} - e^{-i\pi x}}{2i}$.

If it wasn't for the $\frac{\pi}{6}$ term, this wouldn't be a problem for me, but I'm not sure what I can do to fix that.

$\endgroup$
  • 2
    $\begingroup$ Everywhere you see '$x$', in the Euler formula you just place '$\pi t + \frac\pi 6$'. I think you are overcomplicating the question :) $\endgroup$ – jameselmore Sep 1 '15 at 18:42
1
$\begingroup$

Using additional formulas: $$ 2+4\sin(\pi t+\frac{\pi}{6})= 2+4\sin(\pi t)\cos\frac{\pi}{6}+4\cos(\pi t)\sin\frac{\pi}{6}= $$ $$ =2+2\sqrt{3}\dfrac{e^{i\pi^2t} + e^{-i\pi^2t}}{2}+2\dfrac{e^{i\pi^2t} - e^{-i\pi^2t}}{2i}$$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.