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I know arctan (-1) = 3pi/4 but does it also equal 7pi/4?

1 Answer

Sep 11, 2015

...or, alternatively "No"

Explanation:

In order to be treated as a function (which means it can not map into more than one value)
the range of $arctan$ $arctan$ is restricted.

The most common version is that
$XXX - \frac{π}{2} < arctan (θ) \leq \frac{π}{2}$ $color(white)("XXX")-pi/2 < arctan(theta) <= pi/2$
although you will see
$XXX 0 \leq arctan < π$ $color(white)("XXX")0 <= arctan < pi$

The second version is the one you refer to initially
$XXX$ $color(white)("XXX")$ (otherwise $arctan (- 1) = - \frac{π}{4}$ $arctan(-1) = -pi/4$ )
but for neither version is $\frac{7 π}{4}$ $(7pi)/4$ within the defined range.

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