## Related questions with answers

Question

Find the exact radian value. $\\$$\tan ^{-1} 1$

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 2Let $\tan^{-1}1=y$. So, now we have to calculate the value of $y$

$\begin{align*} y&=\tan^{-1}1\\ \tan(y)&=\tan\left(\tan^{-1}1\right)&\textcolor{#4257b2}{\text{Take tangent function both sides}}\\ \tan y&=1&\textcolor{#4257b2}{\text{Simplify}} \end{align*}$

Since tangent of an angle is $1$. So, that angle must be $\dfrac{\pi}{4}$. Because range of tangent inverse function is $\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right]$

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