How do you find the value for ${tan}^{- 1} (- 1)$ $tan ^ -1 ( -1)$ ?

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How do you find the value for ${tan}^{- 1} (- 1)$ $tan ^ -1 ( -1)$ ?

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Answer 1 · 2015-08-02T07:35:41

$- \frac{π}{4}$ $-pi/4$

Explanation:

We know that $tan (- x) = - tan (x) \forall x \in (- \frac{π}{2}, \frac{π}{2})$ $tan(-x) = - tan(x) forall x in (-pi/2, pi/2)$ , and that $tan (\frac{π}{4}) = 1$ $tan(pi/4) = 1$ .

Therefore, $tan (- \frac{π}{4}) = - 1$ $tan(-pi/4) = -1$ , which in turn implies ${tan}^{- 1} (- 1) = - \frac{π}{4}$ $tan^(-1) (-1) = -pi/4$ .

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How do you find the value for ${tan}^{- 1} (- 1)$ $tan ^ -1 ( -1)$ ?

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How do you find the value for ${tan}^{- 1} (- 1)$ $tan ^ -1 ( -1)$ ?