MHB I made 2 equations but can they become 1

[DRMSquared]

So a little background then to the point, I needed to get a cnc machine to do something it don’t want to do, so I came up with 2 equations to lie to the machine to get it to do an operation correctly. It is a radius equation that finds the center point of a radius if it is not a full radius. Can these be combined to make one?

1st: Asin(chord/radius)=x
2nd: radius[sin(x/2)]=y

Y is the input for the machine, it’s the important answer.

 

[Euge]

Welcome, DRMSquared! (Wave)

Can these be combined to make one?

1st: Asin(chord/radius)=x
2nd: radius[sin(x/2)]=y

Y is the input for the machine, it’s the important answer.

In the first equation, does Asin mean the Arcsine, or does it mean $A$ times sin where $A$ is some constant?

 

[DRMSquared]

Welcome, DRMSquared! (Wave)

In the first equation, does Asin mean the Arcsine, or does it mean $A$ times sin where $A$ is some constant?

It would be sin-1 so I’m guessing arcsine

 

[Euge]

Ok. For simplicity, let $C = \text{chord}$ and $r = \text{radius}$. Equation 1 is then $x = \arcsin(C/r)$. Plugging in the expression of $x$ into Equation 2 yields $$y = r\sin(.5\arcsin(C/r))$$

 

[DRMSquared]

Ok. For simplicity, let $C = \text{chord}$ and $r = \text{radius}$. Equation 1 is then $x = \arcsin(C/r)$. Plugging in the expression of $x$ into Equation 2 yields $$y = r\sin(.5\arcsin(C/r))$$

You my friend are awesome, thank you so much, now I can easily plug this into my hp48g and have an easier and quicker time doing this problem.