# How would you write an equation of the cosine function with amplitude 2 and period 6pi?

Jul 9, 2016

$2 \cos \left(\frac{x}{3}\right)$

#### Explanation:

The equation of the cosine function will be of the form

y = acosbx

where amplitude = |a| and period$= \frac{2 \pi}{b}$

here |a| = |2| = 2 and $b = \frac{2 \pi}{6 \pi} = \frac{1}{3}$

Thus equation is $y = 2 \cos \left(\frac{1}{3} x\right)$