Find the value of cot^-1 given arctan

**freestar** · Sep 18th 2011, 03:07 PM

$a = cot^-^1(x)$ given $tan^-^1(x) = \frac{\pi}{4}$

a = ?

No idea where to start I am guessing $cot^-^1 = \frac{1}{tan^-^1}$ but that is probably wrong. Help.

Edit: also tried

$\frac{1}{tan(a)}=x$

$x = tan (\frac{\pi}{4}) = 1$

$\frac{1}{tan(a)} = 1$

$tan(a) = 1$

$a = tan^-^11$

$a = \frac{\pi}{4}$

Not sure if it's right though. Can someone verify please?

**Plato** · Sep 18th 2011, 03:25 PM

Originally Posted by freestar

$a = cot^-^1(x)$ given $tan^-^1(x) = \frac{\pi}{4}$
a = ?
No idea where to start I am guessing $cot^-^1 = \frac{1}{tan^-^1}$ but that is probably wrong. Help.
Edit: also tried
$\frac{1}{tan(a)}=x$
$x = tan (\frac{\pi}{4}) = 1$
$\frac{1}{tan(a)} = 1$
$tan(a) = 1$
$a = tan^-^11$
$a = \frac{\pi}{4}$
Not sure if it's right though. Can someone verify please?

I really have no idea what any of that means.

But: $\text{arccot}(x)=\text{arccot}(0)-\arctan(x).$

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