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HOW DOES THE VALUE OF AN INVERSE COSINE FUNCTION CHANGE WHEN THE UNIT OF ITS ARGUMENT CHANGES? This is an interesting question, especially because the question of units in trigonometric and inverse trigonometric functions is rarely If you’re interested, think this problem through on your own. Then check Problem of the Day 86 In many physics textbooks, the explanation for lift on a flying airplane is that the top of a plane’s wing is longer than the bottom, and so air must travel faster across the top than the bottom, and therefore the pressure is lower above the wing than below. (This difference in pressure caused by different speeds of a moving fluid is a consequence of Bernoulli’s principle.) However, the problem with this explanation is that some planes nevertheless manage to fly upside-down! How could these planes fly both right-side up and upside-down? Could the top of the wing and the bottom of the wing both be shorter than the other when depending on the plane’s orientation? This is absurd, and so there must be something wrong with the explanation. For the correct explanation (briefly, the angle of attack of the wings provides overwhelmingly more lift than any lift produced because of asymmetry in the cross-section of the wing), check out the following references: Well, it’s been a long time since I’ve posted here. I’ve been involved in a number of writing and education projects, and one of The main purpose of QED Infinity is to prepare students to make the difficult transition from high-school mathematics to a lot of mathematics. In my teaching career, I’ve been saddened by the number of students who have been unnecessarily stymied by mathematics issues, sometimes having to drop out of their chosen programs, and other times feeling dumb or being stressed out choice. There are daily exercises, problems, and thoughts to encourage students to do consistent daily work. There are other resources on the site, and I’ll be adding resources gradually as I produce them. For example, my online textbook will be posted to the site later this