Solving Some 'Calculus-Based' Physics Problems with Trigonometry

摘要

College physics textbooks (algebra based) tend to shy away from topics that are usually thought to require calculus. I suspect that most students are just as happy to avoid these topics. Occasionally, I encounter students who are not so easily satisfied, and have found it useful to maintain a storehouse of non-calculus solutions for some common problems. One such type of problem is finding maximums and minimums of functions. A number of authors have presented solutions using, among other techniques, inequalities, geometry, finding the apex of a parabola, or forcing the discriminant of a quadratic equation to be zero; here, I discuss several examples of finding maximums and minimums using trigonometry instead of calculus.