SOLUTION: find the exact value : arctan(tan(-5))

Question 716976: find the exact value : arctan(tan(-5))
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
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.

arctan only returns values between values between -90 and 90 degrees or between and 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 (approximately -1.57) and (approximately 1.57) radians.

If the -5 is radians then what you must do is find an angle that is co-terminal with -5 radians that is between and radians. (Co-terminal angles will always have the same tan's, sin's, etc.)

We can find this co-terminal angle by adding different multiples, possibly including negative multiples, of to -5 radians until we find one and radians.

Since is approximately equal to 6.28, adding to -5 gets us a number approximately equal to 1.28 which is between and radians.

Since we are asked for an exact answer we do not want to use the approximation of 1.27. We use for the exact answer (if the -5 was a number of radians).
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