# Science:Math Exam Resources/Courses/MATH100/December 2010/Question 08

MATH100 December 2010
Other MATH100 Exams

### Question 08

Two points on the surface of the Earth are called antipodal if they are at exactly opposite points (for example, the North Pole and South Pole are antipodal points). Prove that, at any given moment, there are two antipodal points on the equator with exactly the same temperature.

Hint: Let $T(\theta )$ be the temperature, at any given moment, at the point on the equator with longitudinal angle $\theta$ measured in radians, $0\leq \theta \leq 2\pi$ (that is, in one complete trip around the equator, $\theta$ goes from 0 to $2\pi$ ) and consider $f(\theta )=T(\theta +\pi )-T(\theta )$ Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint.

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