On Thu, Jun 07, 2018 at 10:39:06PM -0400, Richard Damon wrote:
First I feel the need to point out that radians are actually fairly fundamental in trigonometry, so there is good reasons for the base functions to be based on radians. The fact that the arc length of the angle on the unit circle is the angle in radians actually turns out to be a fairly basic property.
People managed to use trigonometry for *literally* millennia before radians were invented and named by James Thomson in 1873. Just because they are, *in some sense*, mathematically fundamental doesn't mean we ought to be using them for measurements. We don't write large numbers using powers of e instead of powers of 10, just because exponentiation to base e is in some sense more fundamental than other powers. Even the fact that we talk about sine, cosine and tangent as distinct functions is mathematically unnecessary, since both cosine and tangent can be expressed in terms of sine.
While we are at it, it might be worth thinking if it might make sense to also define a set of functions using circles as a unit (90 degrees = 0.25, one whole revolution = 1)
Hardly anyone still uses grads, and even fewer people use revolutions as the unit of angles. But if you did need revolutions, conveniently many simple fractions of a revolution come out to be whole numbers of degrees, thanks to 360 having lots of factors. All of these fractions of a revolution are exact whole numbers of degrees: 1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/9, 1/10, 1/12, 1/15, 1/18 so I don't believe we need a third set of trig functions for revolutions. -- Steve