Arctangent of Zero is Zero
Jump to navigation
Jump to search
Theorem
- $\arctan 0 = 0$
Proof
By definition, $\arctan$ is the inverse of the tangent function's restriction to $\openint {-\dfrac \pi 2} {\dfrac \pi 2}$.
By Tangent of Zero:
- $\tan 0 = 0$
As $0 \in \openint {-\dfrac \pi 2} {\dfrac \pi 2}$, we have $\arctan 0 = 0$ by the definition of an inverse function.
$\blacksquare$