Question

Is there a formula for sin(x/3)?

Answer 1

I do not think it is likely because it is impossible to trisect an angle exactly in geometry. Since you can not do that I do not know how you could make a construction of right triangles that would lead to a triangle with exactly 1/3 of the original angle in it.

Answer 2

I guess you're right. I was looking forward to finding the value of the sin 1 (deg).

Answer 3

There is the infinite series
sin (x/3) = x/3 - (1/2)(x/3)^2
+ (1/6)(x/3)^3 + ...
-(-1)^n *1/n!* (x/3)^n
(n-> infinity)

Damon has made a good argument that there may be no closed form equation for sin (x/3) in terms of trig functions of x.

I tired Googling sin(x/3) and found nothing

Answer 4

For angles that small, the approximation sin x = x is very good. x must be in radians to use it.

Sin 1 degree = sin pi/180 radian
If you use the first term of the infinite series, that gives you pi/180 = 0.0174533...

The exact value is 0.174524...