# How do you use transformation to graph the cosine function and determine the amplitude and period of y=2cos(1/3x)?

Apr 8, 2018

#### Answer:

Amplitude: $2$ Period: $6 \pi$

#### Explanation:

For a cosine function in the form

$y = A \cos \left(b x\right) ,$ the amplitude is given by $| A |$ and the period by $P = \frac{2 \pi}{b}$

Here, $A = 2 ,$ so the amplitude is $| 2 | = 2$

$b = \frac{1}{3} , P = \frac{2 \pi}{\frac{1}{3}} = 2 \pi \cdot 3 = 6 \pi$