Trig help

[nsaint]

I am a woodworker using segmented cuts to make bowls. Assume the following;
N = Number of sides
S = Slope
MA = Mitre Angle
BA = Blade Angle

In a book I am using the formula to figure out various tool and angle settings is;
Mitre Angle = inverse tan (1 / [ cosS * tan (360 / 2N)])
Blade Angle = inverse tan (cosMA * tanS)

I am trying to put this into a spreadsheet so I can choose various parametrs such as sides and then display the BA and MA values.

The book tells me that a Slope of 15 with 6 sides should result in an MA equal to 60.85 degrees and a BA equal to 7.44 degrees.

How do I get this into excell and do what I am trying to do?

Any help would be greatly appreciated.

[mikerickson]

If you have the number of sides in A1 and the slope in A2, then

=ATAN(1/(COS(RADIANS(A2))*TAN(PI()/A1))) will return the mitre angle.

If you put that formula in B3 then

=ATAN(COS(B3)*TAN(RADIANS(A2))) will return the blade angle.

The difficulty is that these returns are in radians, so the formulas need to be changed to

=DEGREES(ATAN(1/(COS(RADIANS(A2))*TAN(PI()/A1))))

and

=DEGREES(ATAN(COS(RADIANS(B3))*TAN(RADIANS(A2))))

[mdmackillop]

As in

[nsaint]

This was very helpful, but I seemed to run into a snag. If the Slope is set to 90 the blade angle returns 45. In the case where the number of sides = 6, slope = 90, the mitre angle should equal 90 and the blade angle should equal 30, but it doesn't.

The formula appears to work in all other cases except for a slope of 90.

Thoughts?

Also, thanks for the help with this, it seems we are very close and your guidance has been helpful.

[mdmackillop]

Rounding errors
try 89.99
A bit by bit spreadsheet to show what changes.

[nsaint]

Thanks mdmacillop and mikerickson for your help. Yes, I had already used 89.999 to get the desired results, just annoying that I have to do that.

Appreciate your help!

[mdmackillop]

This version contains a little VBA code to change C6 to 89.99 if you enter 90.

[nsaint]

Thanks again for the help. I found a function called CFEET I used to convert my values to feet and inches. I have attached this here just to show what your help has done for me - thanks again.

This forum has been a great help!!

[mdmackillop]

Nice to see the practical implication (and the bowl!)

[mdmackillop]

Because of the code you may get macro security warnings each time you open the workbook. See here (http://vbaexpress.com/forum/showthread.php?t=9545) for how to avoid these.