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 2π.

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 2πz 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 2π1=2π.

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