Interesting angles between 10~~25º ?

[Nik_2213]

TL;DR Summary

Just as there are 'interesting' numbers, per primes, Pythag' triples etc, are there any 'interesting' angles between 10~~25º ??

NOT a home-work / college question, merely wondering...

Just as there are 'interesting' numbers, per primes, Pythag' triples, Euler-stuff etc, are there any 'interesting' angles between 10~~25º ??

I've had a hunt around, noticed several possibilities invoking eg transcendental fractions of radians etc, but...

Ideas ??

 

[jedishrfu]

Only thing I recall is the small angle sin ~ tan approximation for angles of 8 degrees or less.

https://en.m.wikipedia.org/wiki/Small-angle_approximation

 

[fresh_42]

I checked a few Wikipedia pages. These list the most angles between 0° and 30°:
https://de.wikipedia.org/wiki/Sinus_und_Kosinus#Wichtige_Funktionswerte
https://es.wikipedia.org/wiki/Función_trigonométrica

 

[mathman]

Combinations starting with 45 and 30 might be of interest.

 

[jedishrfu]

Also half angles, quarter angles, double angles and sums/differences thereof using the sin/cos angle formulas for summing and differencing angles.

https://mathworld.wolfram.com/TrigonometricAdditionFormulas.html

 

[phinds]

are there any 'interesting' angles between 10~~25º ??

Define "interesting"

 

[fresh_42]

Define "interesting"

inter esse, lat. being between

 

[bob012345]

Irrational angles might be interesting.

 

[mfb]

12 = 60/5 ~ pi/15
15 = 60/4 ~ pi/12
20 = 60/3 ~ pi/9
22.5 = 90/4 ~ pi/8

 

[pbuk]

Irrational angles might be interesting.

Almost all angles are irrational.

 

[bob012345]

Almost all angles are irrational.

It might be interesting that one can make by construction irrational angles and line segments.

 

[fresh_42]

How about: An angle is called interesting iff its sine is in a Galois extension of $\mathbb{Q}.$

 

[jbriggs444]

How about: An angle is called interesting iff its sine is in a Galois extension of $\mathbb{Q}.$

Sorry, I dozed off there. What were you saying again?

 

[fresh_42]

Sorry, I dozed off there. What were you saying again?

That we can draw the darn thing with compass and ruler.