at how many points in the interval -2π, 2π is cos θ at maximum or a minimum? 5 points 3 points 4 points 2…

Explanation:

Step1: Recall cosine - function properties

The cosine function is (y = \cos\theta), and its general form for maxima and minima is (\cos\theta=\pm1). The maxima of (y = \cos\theta) occur when (\theta = 2k\pi), (k\in\mathbb{Z}), and minima occur when (\theta=(2k + 1)\pi), (k\in\mathbb{Z}).

Step2: Find values of (\theta) in the given interval

For the interval ([- 2\pi,2\pi]):

• When (\cos\theta = 1), (\theta=-2\pi,0,2\pi) (using (\theta = 2k\pi), (k=-1,0,1)).
• When (\cos\theta=-1), (\theta =-\pi,\pi) (using (\theta=(2k + 1)\pi), (k = - 1,0)).

Step3: Count the number of points

Counting the points (-2\pi,-\pi,0,\pi,2\pi), we find there are 5 points.

Answer:

5 points