11) [4 marks] GQUOiOF X Show that at any given time there are two antipodal points on the equator with the same temperature. You may assume that temperature varies continuously with position and that the equator is a circle. (Antipodal points are diametrically opposite one another.) y Note: We will assume that the equator is a circle and that a point on the equator can be identied by its standard position angle 6. Let TU?) represent the temperature at the point associated with the angle 6 and let HO?) 2 T(6) T09 + 7r) for 6 E [0,71']. TIUI A T[f}+n] H[0) = T[9]T[B + n] Then H (9) measures the difference of the temperature at pairs of diametrically opposite points. If we can show that there exists 0 such that H (c) = 0 we are done