# How do you find the period and amplitude of y=2/3cos((pix)/10)?

Mar 29, 2017

amplitude is 2/3
period is 20

#### Explanation:

$y = \alpha \cdot \cos \left(x\right)$ period is given as $\left(2 \pi\right)$ and amplitude is $\alpha$
for $y = \cos \left(a x\right)$, period is given as $\frac{2 \pi}{a}$
here, y=$\left(\frac{2}{3}\right) \cos \left(\frac{\pi}{10}\right) x$
so period is $\frac{2 \pi}{\left(\frac{\pi}{10}\right)} = 20$

also, amplitude is $\frac{2}{3}$, because the maximum deviation of curve from the mean is $\frac{2}{3}$ at cos$\left(\frac{\pi x}{10}\right)$ = 1

graph{(2/3)cos((pix)/10)[-10, 10, -5, 5]}