# [Maxima] Finding roots of sextic in radicals

Nikos Apostolakis nikos.ap at gmail.com
Fri Jan 25 11:53:45 CST 2008

```"Raymond Toy (RT/EUS)" <raymond.toy at ericsson.com> writes:

> Nikos Apostolakis wrote:
>> Actually in z3, all sines and cosines occur in the form
>> sin(atan(expr)) and cos(atan(expr)) where expr are some expresions
>> involving square roots.  So using pythagorean theorem one can in
>> principle get an expression involving only radicals from that.
>>
>> So I guess the next question is: is there a global variable that
>> setting it true will cause maxima to simplify sin(atan(x)) to
>> x/sqrt(1-x^2)?
>
>

Great!

> But the expressions aren't sin(atan(x)).  They're sin(atan(x)/3).

Indeed.  I should have been more carefull.

> To simplify that, I think you need to solve a cubic, which will
> probably give another expression containing sin's.
>

Right!  If a = sin(x/3) and c =sin(x) then a is the soloution of the
equation: 3a - 4a^3 = c,

Sorry for the noise,
Nikos

```