Since tangent can spit out any real number, then if there were a real number arctangent didn't accept (i.e., a real number not in the domain of arctan), then arctangent wouldn't achieve this goal! Thus. …

Review your knowledge of the inverse trigonometric functions, arcsin (x), arccos (x), & arctan (x).

Sal introduces arctangent, which is the inverse function of tangent, and discusses its principal range.

I'm going to restrict theta, or my range, to be greater than the minus pi over 2 and less than positive pi over 2. And so if I restrict my range to this right here and I exclude that point and that point.

If we have enough information to use arcsin or arccos, then we also have enough information to figure out the coordinates of the vector and we can just as well use arctan as shown in the video.

Inverse sine (sin − 1) ‍ does the opposite of the sine. Inverse cosine (cos − 1) ‍ does the opposite of the cosine. Inverse tangent (tan − 1) ‍ does the opposite of the tangent.

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I'm going to restrict theta, or my range, to be greater than the minus pi over 2 and less than positive pi over 2. And so if I restrict my range to this right here and I exclude that point and that point.

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