Is there a use for this sort of thing?

Doodling on my calculator - found out that:

logbase2(sin theta) + logbase2(cos theta)=logbase2(sin 2*theta)-1
logbase2(sinh theta)+ logbase2(cosh theta)=logbase2(sin 2*theta)-1
logbase2(sin theta)- logbase2(cos theta)=logbase2(tan theta)
logbase2(sinh theta)- logbase2(cosh theta)=logbase2(tanh theta)

Seeing as I am taking log base2, could this have any applications for
tuning-math?

No, the base is irrelevant; you can remove the log operations
by replacing + with * and - with /.
Then you get standard goniometric equivalences.
What you can see though is when you multiply two
sinewave of the same frequency, you get one an octave higher.

Manuel

--- In tuning-math@yahoogroups.com, "Manuel Op de Coul"
<manuel.op.de.coul@e...> wrote:
>
> No, the base is irrelevant; you can remove the log operations
> by replacing + with * and - with /.
> Then you get standard goniometric equivalences.
> What you can see though is when you multiply two
> sinewave of the same frequency, you get one an octave higher.
>
> Manuel

Only logbase2 gives a difference of 1 though in the first two
equations. Did you mean trigonometric equivalences? Does
sin (theta) * cos (theta)= sin^2 (theta)?

--- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
<paul.hjelmstad@m...> wrote:
> --- In tuning-math@yahoogroups.com, "Manuel Op de Coul"
> <manuel.op.de.coul@e...> wrote:
> >
> > No, the base is irrelevant; you can remove the log operations
> > by replacing + with * and - with /.
> > Then you get standard goniometric equivalences.
> > What you can see though is when you multiply two
> > sinewave of the same frequency, you get one an octave higher.
> >
> > Manuel
>
> Only logbase2 gives a difference of 1 though in the first two
> equations. Did you mean trigonometric equivalences? Does
> sin (theta) * cos (theta)= sin^2 (theta)?

Correction: Line two=logbase2(sinh 2*theta)-1
Correction: sin(theta)* cos(theta)=sin (2*theta)?

Paul G Hjelmstad wrote:
>>Only logbase2 gives a difference of 1 though in the first two >>equations. Did you mean trigonometric equivalences? Does
>>sin (theta) * cos (theta)= sin^2 (theta)?
> > > Correction: Line two=logbase2(sinh 2*theta)-1
> Correction: sin(theta)* cos(theta)=sin (2*theta)?

2*sin(theta)* cos(theta)=sin (2*theta)

http://mathworld.wolfram.com/TrigonometricAdditionFormulas.html

Graham