# What is the period for -3sec(-6x)+2?

Apr 25, 2015

The period is only effected by the argument of the trig function; the other values ($- 3 \text{ and } + 2$ in this case) effect the amplitude and relative location in the plane.

$\sec \left(\theta\right)$ has a period of $2 \pi$

$\sec \left(- 6 x\right) \text{ and } \sec \left(6 x\right)$ have the same period.

$\sec \left(6 x\right)$
is going to cover the same range as $\sec \left(\theta\right)$
but $6$ times "faster"
so
the period of $\sec \left(- 6 x\right)$ is $\frac{2 \pi}{6} = \frac{\pi}{3}$