How do you evaluate arctan(1/2)arctan(12)?

1 Answer
Jun 1, 2015

The arctan(1/2)arctan(12) is the angle thetaθ such that tan(theta) = 1/2tan(θ)=12

We can imagine such an angle in the first quadrant as being part of a right-triangle with opposite side =1=1, adjacent side =2=2, and hypotenuse =sqrt(5)=5.

Unfortunately this is not one of the standard angles and the only way (as far as I can tell) to evaluate it is to use a calculator (or something similar) to look-up:

arctan(1/2) = 0.463648 " radians" = 26.56505^@arctan(12)=0.463648 radians=26.56505