# How do you find the amplitude and period of y=3cospix?

Jul 26, 2017

The amplitude of the function is $3$ and the period is $2$.

#### Explanation:

The standard form of a cosine function is $y = a \cos \left(b x + c\right) + d$, where $a$ is the amplitude, $c$ is the horizontal shift, and $d$ is the vertical shift.

In this equation, $a = 3$, $b = \pi$, $c = 0$, $d = 0$.

The period of a cosine (and sine) function is $\frac{2 \pi}{\left\mid b \right\mid}$.
$\frac{2 \pi}{\left\mid b \right\mid} = \frac{2 \pi}{\left\mid \pi \right\mid} = 2$

So, the amplitude of the function is $3$ and the period is $2$.