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

1 Answer
Jan 7, 2018

The amplitude of cos(x)-6 is 1 and the period is 2pi.

Explanation:

The amplitude of the function, simply put, is the absolute value of the coefficient of cos(x), 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 (2pi)/z in cos(zx). 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 (2pi)/(1)=2pi.

P.S. my explanation is very brief, because I forgot quite a lot of the technical terms, but I hope that would do.