The period of this signal?

Question

can anyone please tell me how can I compute the period of this signal?

Answer 1

$x(t)=1-2\sin(4\pi t) + 6\cos (9\pi t +\frac{\pi}{3} + c)$

If F(x)=sin(ax + c) then period of F(x) is $\dfrac{2\pi}{a}$

So period of $\sin(4\pi t)$ is $\dfrac{2\pi}{4\pi}=\dfrac 12$ and period of $\cos (9\pi t +\frac{\pi}{3} + c)$ is $\dfrac{2\pi}{9\pi}=2/9$

So by taking LCM of both (sin and cos function periods) gives 2 as period of $x(t)$