Question 716976
Since arctan and tan are inverses of each other, the temptation is to think that the answer would be -5. But it depends on whether the -5 is a number of degrees or a number of radians.<br>
arctan only returns values between values between -90 and 90 degrees or between {{{-pi/2}}} and {{{pi/2}}} radians. So if the -5 is degrees then -5 is the answer because -5 degrees is between -90 and 90. But if the -5 is radians then the answer is not -5 because -5 radians is not between {{{-pi/2}}} (approximately -1.57) and {{{pi/2}}} (approximately 1.57) radians.<br>
If the -5 is radians then what you must do is find an angle that is co-terminal with -5 radians that <i>is</i> between {{{-pi/2}}} and {{{pi/2}}} radians. (Co-terminal angles will always have the same tan's, sin's, etc.)<br>
We can find this co-terminal angle by adding different multiples, possibly including negative multiples, of {{{2pi}}} to -5 radians until we find one {{{-pi/2}}} and {{{pi/2}}} radians.<br>
Since {{{2pi}}} is approximately equal to 6.28, adding {{{2pi}}} to -5 gets us a number approximately equal to 1.28 which is between {{{-pi/2}}} and {{{pi/2}}} radians.<br>
Since we are asked for an exact answer we do not want to use the approximation of 1.27. We use {{{2pi + (-5)}}} for the exact answer (if the -5 was a number of radians).