which formula gives the x - coordinates of the maximum values for y = cos(x)?\no (kpi) for any integer…

which formula gives the x - coordinates of the maximum values for y = cos(x)?\no (kpi) for any integer (k)\no (kpi) for (k = 0,pm2,pm4,cdots)\no (\frac{kpi}{2}) for any positive integer (k)\no (\frac{kpi}{2}) for (k = 0,pm2,pm4,cdots)

which formula gives the x - coordinates of the maximum values for y = cos(x)?\no (kpi) for any integer (k)\no (kpi) for (k = 0,pm2,pm4,cdots)\no (\frac{kpi}{2}) for any positive integer (k)\no (\frac{kpi}{2}) for (k = 0,pm2,pm4,cdots)

Answer

Explanation:

Step1: Recall cosine - function properties

The cosine function (y = \cos(x)) has a maximum value of (y = 1).

Step2: Find the x - values for maximum

We know that (\cos(x)=1) when (x = 2k\pi), where (k\in\mathbb{Z}) ( (k = 0,\pm1,\pm2,\cdots)). This can also be written as (k\pi) for (k = 0,\pm2,\pm4,\cdots) since when (k) is an even integer ((k = 2n) where (n\in\mathbb{Z})), (x=2n\pi).

Answer:

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