My professor gave this word problem to us and I can't seem to navigate through all of the directions and hints to understand how to do it. I do know for sure he expects us to use theIntermediate Value Theorem.

Prove that at any instant of time, there are two antipodal points (two

points whose midpoint is the center of the earth) on the equator with the

same temperature, assuming that temperature changes continuously with

the points on earth.

Hints

Picture the equator as a unit circle and set up a coordinate system. Consider

a point P on the circle. We can represent the point P by the angle theta

between the line connecting the origin to the point P and the positive x-axis.

This way, the points on the equator may be labeled by angles theta in [0, 2pi].