My physics professor was able to find the sine of 6 degrees in

>not on the unit circle
are you retarded?

Divine proportions

>>8989834
I don't literally take out a printed copy of the unit circle, I have it all memorized in my head if that's what you're talking about.

If you think I'm retarded for not knowing much more past that then yes, I am retarded.

>>8989843
Every degree is on the unit circle. So if you have it memorized, you would know the answer.

He probably approximated it using Taylor expansion

>>8989814
For small x, sin x ≈ x. Physicists seem to use that kind of approximation a lot.

>>8989814
He's probably autistic about doing arithmetic in his head. Must be a smart man.
>inb4 doing quick math doesn't mean being intelligent
Yes it does. On the other hand, not all smart people can do quick math. It goes only one way

probably the fastest way to find the exact form of sin of any integer is de moivre's theorem and take the imaginary part

>>8989851
>Every degree is on the unit circle. So if you have it memorized, you would know the answer.
Oh, then yeah, I don't have it memorized (just 0, 30, 60, 90 etc. etc.) and I know what you mean. I even learned this but I guess I forgot.

>>8989814
6 degrees is pi/30 radians.

The small angle approximation sin(x)~=x is accurate to within 0.2%. Adding the next term in the Taylor series gives a result that's within ~1ppm:

sin(pi/30)=0.1045284632676534713998341548025
pi/30=0.10471975511965977461542144610932
(pi/30)-(pi/30)^3/6=0.1045283583500282942439678886089

>>8989814
https://math.la.asu.edu/~surgent/mat170/Exact_Trig_Values.pdf

>>8989857
>inb4 doing quick math doesn't mean being intelligent

It literally doesn't. If you think it does then my calculator, phone and computer are the most intelligent entities in the universe along with their fellow electronic brethren.