How would you solve this problem?

 

As can be seen in the figure, light emanates through a fixed arc of angle om measured from one end of the light-emitting aperture to the other. The specifications for the fixtures indicate that 0 m S radians (i.e. the aperture can range from completely closed to open 90 from the vertical). Furthermore, the specifications indicate that the intensity of the light shed by the bulb to a point on the floor (the point P in Figure 1B) varies directly as the sine of some function of the angle o (the angle measured from the vertical to P), so that the sine values reach zero at either end of the light-emitting aperture. The intensity of the light hitting the floor is also dependent on the distance from the bulb to th point on the floor being considered, varying inversely as the square of the distance from the fixture to that point (the point P in Figure 1B). The intensity of the light reaching the point P is therefore the product of these two effects. To properly plan the positioning of these fixtures, we need you to construct a model of the light's intensity / as a function of o. Specifically, we want to know where (by way of angle) on the floor under the fixtures the intensity of light is the greatest.