Answer to Question #87411 in Trigonometry for Rena

Question

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Answer 1

Evaluate $\tan^{-1} 1.$

Solution. By the definition of the inverse trigonometric function $\tan^{-1}$ we have that

$$\tan(\tan^{-1}(x))=x$$

for every real number $x.$ Therefore from $\tan(\frac{\pi}{4})=1$ we have

$$\tan^{-1}1=\frac{\pi}{4}.$$