Amazing! Penn Professor Discovers That Sine-Squared Is a Parabola


Photo by Ttrung / Public Domain

It was shaping up to be just another PHYS 150 lecture. But then, inspiration suddenly struck Professor Chuck Jackson, who was writing out the small angle approximation for the sine function on the board.

"In physics, we often say that sin(x) = x for small values of x," explained Jackson. "Over the years, I've taught the concept so much that I've just kind of internalized it to mean that sin(x) is always x. We use this idea quite a lot in physics."

In fact, Jackson uses this idea so much that he has been known to take off points when students don't immediately replace sin(x) with x when solving equations. Even when the problem requires integrating the sine function from zero to pi.

"Sin(x) is x! Sin(x) is x!" Jackson continued, growing increasingly more excited. "So we can also approximate the square of sin(x) is a parabola with a vertex at the origin, because the square of sin(x) is x-squared."

And since x = sin(x) for all values of x, Jackson believes that we may as well replace all instances of "x" with the sine function. "There should be no more functions of x, only of sin(x). We ought to differentiate functions with respect to sin(x). Think of the possibilities!"