How do you evaluate $arctan (\frac{1}{2})$ $arctan(1/2)$ ?

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How do you evaluate $arctan (\frac{1}{2})$ $arctan(1/2)$ ?

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Answer 1 · 2015-06-01T23:21:21

The $arctan (\frac{1}{2})$ $arctan(1/2)$ is the angle $θ$ $theta$ such that $tan (θ) = \frac{1}{2}$ $tan(theta) = 1/2$

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 $= \sqrt{5}$ $=sqrt(5)$ .

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:

$arctan (\frac{1}{2}) = 0.463648 radians = {26.56505}^{\circ}$ $arctan(1/2) = 0.463648 " radians" = 26.56505^@$

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How do you evaluate $arctan (\frac{1}{2})$ $arctan(1/2)$ ?

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