Is ArcTan(-1) equal to both 7pi/4 and 3pi/4?

[Miike012]

Homework Statement

ArcTan(-1) = theta
I figured that theta was both 7pi/4 and 3pi/4.. but the book has -pi/4

Because my two answers are both equivalent to -pi/4 would I be wrong?

Homework Equations

The Attempt at a Solution

 

[Ryker]

Yes, only -pi/4 is the correct answer, because the range of the arctan function is from -pi/2 to pi/2. If for x = -1, you would get more than one y, then that would mean that the function is not well-defined, ie. that arctan is not a function at all. I don't know how you defined arctan in school, but it is the inverse function not of tanx, but of tanx on (-pi/2, pi/2).

You are right in thinking that tan(3pi/4) = tan(7pi/4) = tan(-pi/4), though.

 

[Miike012]

O duh that makes sence..

So say I had ... ArcTan(X) = Y
X could be all real numb and Y has to be inbetween -90 and 90 right?

 

[Ryker]

Exactly. Just be careful when you say between -90 and 90, because in degrees that's true, but when you look at the y-axis, you'll have the angle in radians. Try to think of angles in radians when doing these things, and just consider degrees to help you.

 

[Miike012]

Ok thank you.