Question 970477
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Evaluate cos[arctan(-5/12)].
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        In the post by @lwsshak3 the answer is incorrect and reasoning is also incorrect.

        See below my correct solution.



Function arctan has values in the interval ({{{-pi/2}}},{{{pi/2}}}).


Therefore, the problem asks to evaluate cos(x), given that 'x' is in the fourth quadrant
(not in the second quadrant, as @lwsshak3 mistakenly assumes) and tan(x) = -5/12.


So, let x=angle in QIV whose tan is (-5/12)
tan(x) = (-5/12) (working with a (5-12-13) right triangle in quadrant IV)
cosine is positive in QIV; therefore
cos[arctan(-5/12)] = cos(x) = 12/13.


<U>ANSWER</U>.  cos[arctan(-5/12)] = 12/13.


Solved correctly.