# How do you find the amplitude and period of y=sec(1/3theta)?

Oct 21, 2017

Amplitude = None, Period = $6 \pi$

#### Explanation:

Use the standard form $y = a \left(\sec b x - c\right) d$ equation, where
Amplitude = a, Period = $\frac{2 \pi}{b}$, Phase shift = c/b & vertical shift = d.

Given equation is $y = \sec \left(\left(\frac{1}{3}\right) \theta\right)$

Since the graph of the function sec does not have a maximum or minimum value, there can be no value for the amplitude.
Amplitude = none

Period $= \frac{2 \pi}{b} = \frac{2 \pi}{\frac{1}{3}} = 6 \pi$

Phase shift = c / b = 0 as ( c = 0)

Vertical shift = d = 0.