**Inverse Tangent tan ^{-1} Tan^{-1} arctan Arctan**

The inverse function of tangent.

**Basic idea**: To find tan^{-1} 1, we ask "what angle has tangent equal to 1?" The answer is 45°. As a result we say that ^{-1} 1 = 45°.^{-1} 1 = π/4.

**More**: There are actually many angles that have tangent equal to 1. We are really asking "what is the simplest, most basic angle that has tangent equal to 1?" As before, the answer is 45°. Thus ^{-1} 1 = 45°^{-1} 1 = π/4.

**Details**: What is ^{-1} (–1)?^{-1} (–1) = –45°^{-1} (–1) = –π/4.

In other words, the range of tan^{-1} is restricted to

**Note**: arctan refers to "arc tangent", or the radian measure of the arc on a circle corresponding to a given value of tangent.

__Technical note__: Since none of the six trig functionssine, cosine, tangent, cosecant, secant, and cotangent are one-to-one, their inverses are not functions. Each trig function can have its domain restricted, however, in order to make its inverse a function. Some mathematicians write these restricted trig functions and their inverses with an initial capital letter (e.g. Tan or ^{-1}).

**See also**

Inverse trigonometry, inverse trig functions, interval notation

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