How do you find the exact value of #Arctan(1/2)#?
these are calculator values
In [0, 2
tan x can be any number on the real line, including rational numbers i.e. integer/integer.
Inversely, the angle(s) are transcendental numbers (sans 0 for 0), in radian measure, that might approximate to rational numbers, in degree measure. For example, arctan 1 =
This is a matter of our convenience, by dividing
is the best expression for the exact value of
There's essentially no way to find an "exact" value of
By the typically vacuous arithmetic of the real numbers
is the exact value of
In general the relationship between a slope (which is what a tangent is) and an angle is transcendental. Among rational tangents, only