How do you find the exact value of $arctan 1$ $arctan 1$ ?

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Answer 1 · 2017-07-13T14:29:05

$arctan 1 = \frac{π}{4}$ $arctan 1 = pi/4$

Based on the definition of $arctan$ $arctan$ , you know that $tan θ = 1$ $tan theta = 1$ ; therefore, $arctan 1 = θ$ $arctan 1 = theta$ .

The only values of $θ$ $theta$ that make the equation $tan θ = 1$ $tan theta = 1$ true are $\frac{π}{4}$ $pi/4$ and $\frac{5 π}{4}$ $(5pi)/4$ .

However, we must consider the range of the $arctan$ $arctan$ function, which is $(- \frac{π}{2}, \frac{π}{2})$ $(-pi/2, pi/2)$ .

Only $\frac{π}{4}$ $pi/4$ falls into this interval. Thus, $arctan 1 = \frac{π}{4}$ $arctan 1 = pi/4$ .

How do you find the exact value of arctan 1arctan1arctan 1?