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

which formula gives the x - coordinates of the maximum values for y = cos(x)?\n$k\\pi$ for any integer $k$\n$k\\pi$ for $k = 0,\\pm2,\\pm4,...$\n$\\frac{k\\pi}{2}$ for any positive integer $k$\n$\\frac{k\\pi}{2}$ for $k = 0,\\pm2,\\pm4,...$

which formula gives the x - coordinates of the maximum values for y = cos(x)?\n$k\\pi$ for any integer $k$\n$k\\pi$ for $k = 0,\\pm2,\\pm4,...$\n$\\frac{k\\pi}{2}$ for any positive integer $k$\n$\\frac{k\\pi}{2}$ for $k = 0,\\pm2,\\pm4,...$

Answer

Explanation:

Step1: Recall cosine - function properties

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

Step2: Find the x - values for maximum

We know that (\cos(x)=1) when (x = 2k\pi), where (k\in\mathbb{Z}) (the set of all integers). We can rewrite (2k\pi) as (k\pi) where (k = 0,\pm2,\pm4,\cdots) (even integers).

Answer:

(k\pi) for (k = 0,\pm2,\pm4,\cdots)