# [Python-ideas] Trigonometry in degrees

Steven D'Aprano steve at pearwood.info
Fri Jun 8 02:11:39 EDT 2018

```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
```