# Thread: Exact Value of arctan (-2)

1. ## Exact Value of arctan (-2)

Hi,

I don't know how to find the exact value of arctan (-2). By graphing, I know that it's approximately -1.107 (tan -1.107 = -2), but is there a simpler exact version of that, like 2pi/3 or 1/sqrt(3)? I can't find it in any trig chart and I don't know of any way to derive it from the known values in a trig chart.

2. Originally Posted by greenstupor
Hi,

I don't know how to find the exact value of arctan (-2). By graphing, I know that it's approximately -1.107 (tan -1.107 = -2), but is there a simpler exact version of that, like 2pi/3 or 1/sqrt(3)? I can't find it in any trig chart and I don't know of any way to derive it from the known values in a trig chart.
Why do you need the exact value? No-one is ever going to ask you for it! It is so tedious and difficult to get that I'm not even going to bother even beginning to explain it. You will find information using Google.

3. Haha. Okay, I'll assume that my math teacher won't ask for it either, then. My current homework is about converting Cartesian coordinates to polar, and every single problem has had an exact transfer (i.e., no decimals) except for this one (the Cartesian coordinate is (1, -2), btw). So I guess I'll just put the polar conversion as (sqrt(5), arctan(-2)) or something like that.

Thanks for the input!

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### tan 1.107

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