which formula gives the x - coordinates of the maximum values for y = cos(x)?\n○ kπ for any integer k\n○ kπ…

Answer:

A. $k\pi$ for any integer $k$

Explanation:

Step1: Recall cosine function properties

The cosine function $y = \cos(x)$ has a range of $[- 1,1]$.

Step2: Identify maximum - value points

The maximum value of $y=\cos(x)$ is $y = 1$.

Step3: Find x - coordinates for maximum

We know that $\cos(x)=1$ when $x = 2k\pi$, where $k\in\mathbb{Z}$ (set of all integers). Also, $\cos(x)$ has the same maximum value at $x = 0,\pm2\pi,\pm4\pi,\cdots$ which can be written in the general form $x = k\pi$ where $k$ is an even integer (a subset of all integers). In general, for the maximum values of $y = \cos(x)$, the $x$-coordinates are given by $x = 2k\pi$ (a special case of $k\pi$ when $k$ is even). So the $x$-coordinates of the maximum values of $y=\cos(x)$ are $k\pi$ for any integer $k$.