I'm trying to remember the formula for a semi-circle using sin and cos.

[ronhollenbeck]

I'm trying to remember the formula for a semi-circle using sin and cos. I need it in a form that I can use with one of the online graphing calculators. I know (4-x^2)^0.5 works but I am looking for a sin and cos formula that does the same thing.

 

[Dr.Peterson]

I'm trying to remember the formula for a semi-circle using sin and cos. I need it in a form that I can use with one of the online graphing calculators. I know (4-x^2)^0.5 works but I am looking for a sin and cos formula that does the same thing.

Which calculator are you using, and what form does it require? Are you saying that using y = (4-x^2)^0.5, or equivalently y = sqrt(4-x^2), doesn't work? Or is there just some reason you prefer a different form?

The main reason for using sin and cos would be if you want a parametric form, which I wouldn't expect you to need. You could, I suppose, use y = r sin(arccos(x/r)), which amounts to converting a polar form to rectangular, but that seems like overkill.

 

[Steven G]

I'm trying to remember the formula for a semi-circle using sin and cos. I need it in a form that I can use with one of the online graphing calculators. I know (4-x^2)^0.5 works but I am looking for a sin and cos formula that does the same thing.

One form of an equation of a circle is x² + y² = r². Just solve this for y and use the + or - sign to get the equation for a semi-circle.

 

[Dr.Peterson]

One form of an equation of a circle is x² + y² = r². Just solve this for y and use the + or - sign to get the equation for a semi-circle.

That appears to be what the OP did to get y = sqrt(4-x^2), with r = 2. And as far as I can see, that should be all that is needed. We have to wait and find out why a formula with sin and cos is wanted; as I suggested, it might be a parametric form: x = cos(t), y = sin(t).

 

[Steven G]

That appears to be what the OP did to get y = sqrt(4-x^2), with r = 2. And as far as I can see, that should be all that is needed. We have to wait and find out why a formula with sin and cos is wanted; as I suggested, it might be a parametric form: x = cos(t), y = sin(t).

Yes yes, now the OP needs to use the transformation you stated (x= cos(t) and y =sin (t)). Also I *think* that the OP wanted a general formula for the semi-circle using sines and cosines.

 

[ronhollenbeck]

Which calculator are you using, and what form does it require? Are you saying that using y = (4-x^2)^0.5, or equivalently y = sqrt(4-x^2), doesn't work? Or is there just some reason you prefer a different form?

The main reason for using sin and cos would be if you want a parametric form, which I wouldn't expect you to need. You could, I suppose, use y = r sin(arccos(x/r)), which amounts to converting a polar form to rectangular, but that seems like overkill.

I'm using the graphing calculator at desmos.com/calculator. I knew there was a sin/cos formula for a semicircle but couldn't remember it. I just wanted to satisfy my curiosity.

 

[ronhollenbeck]

Thanks Dr.Peterson, y=r*sin(arcos(x/r)) works. I'm using the graphing calculator at desmos.com/calculator. I wanted to know the formula just to satisfy my curiosity.