Consider the function

MATHEMATICS · Subjective · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

y=\cos x

. (i) List all

x

–intercepts of the graph for

x\in[-2\pi,2\pi]

. (ii) Find the coordinates of every maximum and minimum point of the graph in the same interval. (iii) Construct a table of ordered pairs

(x,y)

containing at least eight key points that would be sufficient to produce an accurate sketch of the graph on the interval

[-2\pi,2\pi]

. Your table must include all points obtained in parts (i) and (ii). (iv) Using the information from parts (i)–(iii), sketch the graph of

y=\cos x

for

x\in[-2\pi,2\pi]

on a pair of perpendicular axes. Label clearly the intercepts, maxima, minima and end points of the interval.