Suppose I have the function:
$u(t,x)=sin(x)cos(2t)+cos(x)sin(t)cos(t)$
How can I know if this function is a periodic function of $t$ if it includes two variables?
Multivariable periodic function?
0
$\begingroup$
multivariable-calculus
trigonometry
periodic-functions
-
0$\sin t \cos t = \frac 12 \sin 2t$ – 2017-02-17
-
0it must be periodic in $t$ for all values of $x$ – 2017-02-18
1 Answers
0
$u(t+2\pi,x) = \sin(x) \cos(2(t+2\pi)) + \cos(x) \sin(t + 2\pi) \cos(t + 2 \pi) = \sin(x) \cos(2t) + \cos(x) \sin(t) \cos(t) = u(t,x)$
In fact we have $u(t+\pi,x) = u(t,x)$.