# How do you find the amplitude and period of y=2sec(4/5theta)?

Jun 24, 2017

Amplitude is $2$.
Period is $\frac{5 \pi}{2}$ or $7.85398163$.

#### Explanation:

Standard Form: $y = a \sec b \left(x - c\right) + d$
Equation: $y = 2 \sec \left(\frac{4}{5} \theta\right)$
$a = 2$
$b = \frac{4}{5}$
$c =$none
$d =$none

AMPLITUDE
amplitude = distance from middle of graph (y=0) to highest and lowest points on graph
formula: $| a |$
$| 2 |$
$2$
Amplitude is $2$.

PERIOD
period = interval in which the graph repeats itself
formula: $\frac{2 \pi}{|} b |$
$\frac{2 \pi}{|} \frac{4}{5} |$
$\frac{2 \pi}{\frac{4}{5}}$
$2 \pi \div \frac{4}{5}$
$2 \pi \cdot \frac{5}{4}$
$\frac{10 \pi}{4}$
$\frac{5 \pi}{2} = 7.85398163$
Period is $\frac{5 \pi}{2}$ or $7.85398163$.