# How do you use transformation to graph the cosine function and determine the amplitude and period of y=cos(x)-6?

Jan 7, 2018

The amplitude of $\cos \left(x\right) - 6$ is 1 and the period is $2 \pi$.
The amplitude of the function, simply put, is the absolute value of the coefficient of $\cos \left(x\right)$, because that number is quite literally the distance from a crest to the equilibrium, which is also the definition of amplitude. Given that the coefficient is 1, the amplitude is 1.
The period is given by $\frac{2 \pi}{z}$ in $\cos \left(z x\right)$. This is because the coefficient $z$ indicates the amount of horizontal compression of the graph. Given that $z = 1$ in this case, the period is $\frac{2 \pi}{1} = 2 \pi$.