help with inverse tangent

**hashshashin715** · December 15th 2011, 05:13 PM

Which value of a will make this true?

-2w = -arctan( w / a) ?

**skeeter** · December 15th 2011, 06:00 PM

Originally Posted by hashshashin715

Which value of a will make this true?

-2w = -arctan( w / a) ?

where did this equation come from?

**sbhatnagar** · December 18th 2011, 05:58 AM

$\begin{align*}-2w &=-\tan^{-1}{\left( w \over a \right)} \\2w &=\tan^{-1}{\left( w \over a \right)}\\ \tan(2w) &= \frac{w}{a} \\ a &=w \cdot \cot(2w) \end{align*}$

The equation is true for $a=w\cdot \cot{(2w)}$ .

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