I am trying to compute the amount of energy received by the Earth from the sun, by integrating over the Earth's surface. I keep reading that the formula should be: E = e-max * cos @ * area e-max is the solar insolation, @ is the angle between the sun and the perpendicular to the land, @=0 at noon (at equator) It's the cosine that I am having trouble with. What is wrong about the following argument against a factor of cosine for the received energy? Cosine changes fastest at cos @ = 0, and slowest at cos @ = 1. That means that at sunrise(SR) and sunset(SS), the amount of sun that the land gets is changing most rapidly, and at noon(N) least rapidly. When I picture a mental image of the Earth rotating about its axis, it seems to me that the change in amount of sun at SR, SS, and N should be the same, should all be at a minimum, and at +/- 45 deg should be at a maximum. That would correspond to cos^2, not cos. It also seems that the factor at +/- 45 should be half of the maximum, by symmetry. A factor of cosine means half of e-max occurs at @=60, which seems anti-intuitive.