# How do you find the period of y = -10cos((pi x)/6)?

Oct 15, 2016

The period is 12.

#### Explanation:

$y = - 10 \cos \left(\textcolor{red}{\frac{\pi}{6}} x\right)$

The general form of a cosine equation is

$y = A \cos \left(\textcolor{red}{B} x - C\right) + D$ where

$A =$ amplitude

$\frac{2 \pi}{\textcolor{red}{B}} =$ the period

$\frac{C}{B} =$ the phase shift

$D =$ the vertical shift

In our example, $\textcolor{red}{B} = \textcolor{red}{\frac{\pi}{6}}$ and

the period $= \frac{2 \pi}{\textcolor{red}{B}} = \frac{2 \pi}{\textcolor{red}{\frac{\pi}{6}}} = 2 \pi \cdot \frac{6}{\pi} = 12$