the productivity of a person at work is modeled by a cosine function: 5cos (pie/2 (t)) +5, where t is in hours. If the person starts work at t=0, being 8:00 am, at what times is the worker the least productive?

Answer 1

P = 5cos (pie/2 (t)) +5
the period of this function is 2π/(π/2) = 4

for the lowest productivity, we need the minimum of the function.
we know that cos (pie/2 (t)) has a minimum of -1
then 5cos (pie/2 (t))has a minimum of -5
and 5cos (pie/2 (t)) +5 has a minimum of 0

so when is 5cos (pie/2 (t)) +5 = 0 ?
5cos (pie/2 (t)) = -5
cos (pie/2 (t)) = -1
but cos π = -1

π/2t = π
t/2 = 1
t = 2

look at the graph:
http://www.wolframalpha.com/input/?i=plot+y++%3D+5cos+(%CF%80%2F2+(t))+%2B5

notice a minimum at t = 2

translate that into a time of 10:00 am