## Thomas' Calculus 13th Edition

$T=6$
When we are presented with a function such as $sin(bx)$ and are asked to find the period, it is useful to make use of the following formula: $\frac{2\pi}{T}=b$ The $T$ in the equation represents the period of the function, as in the amount of $x$ units before the function repeats itself. In this question, we have $-sin(\frac{\pi x}{3})$. Keep in mind that while function does have a negative sign in front of it, it does nothing to alter the period, as it simply reflects the function about the x-axis, but no *change in the period*. Thus, $\frac{2\pi}{\frac{\pi}{3}}=T=6$ . Keep in mind that the formula above allows us to easily swap the $T$ and the $b$ in the formula, thus, the period of this function is $6$.