# How do you use transformation to graph the cosine function and determine the amplitude and period of y=3cosx?

May 6, 2018

The amplitude is $3$ and the period is $2 \pi$

#### Explanation:

The most general cosine-like function that you can have is

$A \cos \left(\setminus \omega x + \phi\right) + b$

where:

• $A$, as a multiplicative factor, affects the amplitude of the wave. The amplitude is exactly $A$.
• $\omega$ affects the period of the wave. The period is $\frac{2 \pi}{\omega}$.
• $\phi$ is the shift of the wave. It affects the wave by horizontal translation.
• $b$ is also a shift, but vertical.

If we want to have

$A \cos \left(\setminus \omega x + \phi\right) + b = 3 \cos \left(x\right)$

it means that we have chosen $A = 3$, $\omega = 1$. $\phi = 0$ and $\beta = 0$.