1. ## Re-arranging equation

Hi,

Any help re-arranging the equation below would be greatly appreciated

The following equation needs re-arranging to work out alpha (a)

Phase max = 90 - (2 * tan-1 (sqrt a))

In the actual problem my phase max = 14.14 and I know that the value of alpha (a) should work out to be 0.6072
I need to be able to derive the equation above in an upcoming exam so any help would be appreciated

Thanks

Dave

2. ## Re: Re-arranging equation

Originally Posted by db52174
Hi,

Any help re-arranging the equation below would be greatly appreciated

The following equation needs re-arranging to work out alpha (a)

Phase max = 90 - (2 * tan-1 (sqrt a))

In the actual problem my phase max = 14.14 and I know that the value of alpha (a) should work out to be 0.6072
I need to be able to derive the equation above in an upcoming exam so any help would be appreciated

Thanks

Dave
I'm going to call "Phase max" P for convenience.

First isolate the inverse tangent:
$P = 90 - (2~tan^{-1} (\sqrt a))$

$tan^{-1} (\sqrt a) = \frac{90 - P}{2}$

$tan \left ( tan^{-1} (\sqrt a) \right ) = tan \left ( \frac{90 - P}{2} \right )$

Can you take it from here?

-Dan