Find the fundamental period of $$\sin \bigg(\frac{3x}{5}\bigg) + \sec \bigg(\frac{2x}{7}\bigg) + \bigg\{\frac{2x}{\pi}\bigg\}$$ where $\{\cdot\}$ is the fractional part function.
Hello,
I solved this problem using LCM approach.
Period of $\sin \big(\frac{3x}{5}\big) = 2 \pi \cdot \frac{5}{3} = \frac{10 \pi}{3}$
Period of $\sec \big(\frac{2x}{7}\big) = 7 \pi$
Period of $\big\{\frac{2x}{\pi}\big\} = \frac{\pi}{2}$
LCM = $70 \pi$.
So, $70 \pi$ is the period of this function, but I have trouble proving that this is the fundamental period. Is this the fundamental period, and if so, how can we prove this?
Thanks.