arctan (-1) =?

Question

I know arctan (-1) = 3pi/4 but does it also equal 7pi/4? My book only lists 3pi/4 as an answer...
When you write 3pi/4 as the answer, is 7pi/4 implied? Or am I wrong and arctan (-1) is not equal to 7pi/4? Please explain.
Thanks

Oh..ok, thanks. What about this:
arccos(1/2)
In my book, it says the answer is pi/3. However, can't it also be -pi/3 whic is 5pi/3? When do you put the (-) symbol and when do put the positive symbol?

Oh... now I understand. Thanks Edgar Greenberg

Answer 1

No, arctan (x) is only defined from -π/2 to π/2, so that it is a one to one function. Therefore arctan(-1) can only = -π/4.

Responce to EDIT: The definitions of the range of each arcfunction depends on the arcfunction, and sometimes also the textbook you look it up in. The wikipedia link has the principal definitions.

Answer 2

You're right. The tangent function repeats itself every pi radians, so if the solution to "arctan (x)" is "y", then y+pi, y-pi, y+2pi, etc, are also acceptable solutions. Usually, textbooks only list the smallest solution; in this case, 3pi/4. If you have a math teacher that actually cares about what they're doing, though, then 7pi/4 should also work.

Answer 3

Arctan (-1) = -45 degrees.

Answer 4

actually arctan (-1) = -π/4
The angle whose tangent is -1 = 3π/4 ± nπ

arctan(x) is a function
It is only defined over the open interval (-π/2, π/2)
That is why it it is differentiable for all x.

Answer 5

The arctangent is the angle whose tangent is equal to the given value. In other words, the inverse tangent function.

Go to: http://www.math.com/tables/algebra/functions/trig/overview.htm

The above link should help more in detail.

Guido

Answer 6

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