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?

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

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)

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...

To find the greatest possible slope of a line drawn from the origin to one of the points where the graphs of y = 1/2 and y = cos(x) intersect, we need to determine the points of intersection first.

Setting the two equations equal to each other, we have:

1/2 = cos(x)

To find the solutions for this equation, we need to consider the range of the cosine function, which is -1 to 1. Since the value of the cosine function never exceeds 1, the equation 1/2 = cos(x) has no real solutions.

Therefore, there are no intersection points between the graphs of y = 1/2 and y = cos(x). As a result, it is not possible to draw a line with a slope from the origin to any intersection point. Thus, there is no greatest possible slope for such a line.