Mathematics

Problem

(Counting zeros and extrema of

\cos x

) a. (i) In the interval

\left[-\dfrac{7\pi}{2},\, \dfrac{9\pi}{2}\right]

, list all the zeros of

y=\cos x

. b. (ii) Find the coordinates of each maximum and minimum point of

y=\cos x

within the same interval. c. (iii) Calculate the total number of extrema (both maxima and minima together) that occur for

y=\cos x

between

x=-\dfrac{7\pi}{2}

and

x=\dfrac{9\pi}{2}