Question

What is the amplitude of \(y = \cos\left(\frac{2\pi}{5}x\)\)?

a. \(a\)

b. \(\frac{2\pi}{5}\)

c. \(b\)

d. \(1\)

Answer 1

The amplitude of
`\(y = \cos\left((2\pi)/(5)x\)\))` is 1.(Option d)

Step-by-step explanation:

In a trigonometric function like
`\(y = \cos(ax)\)`, where a represents the coefficient of x, the amplitude is the coefficient of the trigonometric function (in this case, cosine), which is 1.(Option d) The amplitude of a cosine function determines the maximum distance between the function's peak and its average value.

It signifies the highest value that the function reaches above or below its average value, which, for cosine functions, ranges from -1 to 1. The coefficient a in this context
`(\((2\pi)/(5)\))` represents the frequency, not the amplitude. The amplitude remains constant for cosine functions and is independent of the coefficient of x. (Option d)

The amplitude of a trigonometric function corresponds to its highest value above or below the mean, which for cosine functions is 1 and −1, indicating the highest and lowest points reached in the function. In this case, regardless of the coefficient a alongside x, the amplitude remains 1 for the cosine function.