Use the graph of the function to answer the following.

Question

f(x) = cos(x) on the interval [−2𝜋, 2𝜋]

(a) Find the x-intercepts of the graph of y = f(x). (Enter your answers as a comma-separated list.)

x =



(b) Find the y-intercepts of the graph of y = f(x).(Enter your answers as a comma-separated list.)

y =

(c) Find the intervals on which the graph of y = f(x) is increasing and the intervals on which the graph of y = f(x) is decreasing. (Enter your answers using interval notation.)

increasing:

decreasing:

(d) Find the relative extrema of the graph of y = f(x). (Enter your answers as a comma-separated list of ordered pairs.)

relative maxima:

relative minima

Answer 1

x intercepts are when y = zero

cosx=0 when x = pi/2 + 2npi where n = any integer that makes x fall in the domain -2pi<x<2pi

x=pi/2, 3pi/2, -pi/2 and -3pi/2 or 90, 270, -90 and -270 degrees

or as points they are (3pi/2,0), (pi/2,0), (-pi/2,0), and (-3pi/2,0)

just one y intercept, y=1, or the point (0,1)

cosx=1 when x=0

cosx is increasing over the intervals (-p,0,) and (pi,2pi)

cosx is decreasing over the intervals (-2p,-pi) and (0,pi)

relative or local and global maximums are (-2pi,1), (0,1) and (2pi,1)

relative or local and global minimums are (-pi,-1), (pi,0)

Answer 2

a) pi/2, 3pi/2, -pi/2, -3pi/2

b) 1

c)

increase: (-pi, 0), (pi, 2pi)

decrease: (0, pi), (-2pi, -pi)

d)

relative maxima: (-2pi,1), (0,1), (2pi,1)

relative minima: (-pi,-1), (pi,1)