How do you evaluate $arctan (1)$ $arctan(1)$ ?

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How do you evaluate $arctan (1)$ $arctan(1)$ ?

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Answer 1 · 2016-08-13T08:30:57

$= 45^{\circ}$ $=45^@$
$= \frac{π}{4}$ $=pi/4$

Explanation:

$arctan (1)$ $arctan(1)$
$= {tan}^{- 1} (1)$ $=tan^-1(1)$
$= 45^{\circ}$ $=45^@$
$= \frac{π}{4}$ $=pi/4$

Answer 2 · 2016-08-13T08:45:11

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

Explanation:

$color(white)()$
$θ = arctan (1)$ $theta = arctan(1)$ is the angle $θ \in (- \frac{π}{2}, \frac{π}{2})$ $theta in (-pi/2, pi/2)$ satisfying $tan (θ) = 1$ $tan(theta) = 1$

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Note that the triangle formed by bisecting a unit square diagonally is a right angled triangle with sides $1$ $1$ , $1$ $1$ , $\sqrt{2}$ $sqrt(2)$ and angles $\frac{π}{4}$ $pi/4$ , $\frac{π}{4}$ $pi/4$ and $\frac{π}{2}$ $pi/2$ .

So we find:

$tan (\frac{π}{4}) = \frac{opposite}{adjacent} = \frac{1}{1} = 1$ $tan(pi/4) = "opposite"/"adjacent" = 1/1 = 1$

So $θ = \frac{π}{4}$ $theta = pi/4$ satisfies $tan (θ) = 1$ $tan(theta) = 1$ and is in the required range.

$color(white)()$
So:

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

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How do you evaluate $arctan (1)$ $arctan(1)$ ?

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