The graph of y=1/2 and the graph of y=cosx intersect in an infinite number of points. What is the greatest possible slope of a line drawn from the origin to one of these points?

Answer 1

I you make a sketch you will find the the greatest slope (the steepest) happens at the first intersection point.
that is, when x = π/6
(cos π/6 = 1/2)

so the intersection point is (π/6 , 1/2)
so find the slope from (0,0) to that point

Answer 2

how did you get pi/6??

when i graphed it (on a calc in "radians" mode) i got the first intersection point at (1.04...., .5)

Answer 3

You are right, my error
cos 60° = 1/2
and 60° is π/3 radians not π/6

so the point is (π/3 , 1/2)

btw, π/3 = 1.047...