Is sin(7t) + 2sin(10t) Periodic, if yes what is the period or angular frequency?
Is cos(2t) + cos ( 2 * pi * t) Periodic?
How exactly can we tell if a function is periodic without graphing it?
Thanks in advance.
sin(7t) is periodic with period 2pi/7 while 2sin(10t) is periodic with period 2pi/10. The smallest number, which is a multiple of both periods, that is, of 2pi/7 and 2pi/10, is 2pi, which is then the period of the sum.
For the other problem, cos(2t) has period pi, while cos(2pi*t) has period 1. There is no number, which is an integer multiple of both of these periods, so the function cos(2t) + cos(2pi*t) is not periodic.