Quandaries and Queries


I am a programmer trying to calculate the following.
What is the formula to find the cross-sectional area of a cylinder with out using any trig functions? or better yet, how can you calculate any given volume in a cylindrical tank with spherical heads with out trig functions?
I am using a PLC (programmable logic controller) to do this and trig functions are not available.


Hi Derek,

I was hoping that there was a way to do this without trig functions but when you explained the problem more completely I think that trig functions are unavoidable. There is however a way to approach this problem differently. I would use trig functions to find an expression for the area or volume you need and then evaluate the expression by approximating the trig functions, perhaps using Taylor series. For example if you need to calculate tan(x) near x = pi/4 you can use (you need to express the angles in radians)

tan(x) = 1 + 2(x - pi/4) + 2(x - pi/4)28/3(x - pi/4)3

as an approximation. You may need only two or three terms of the expression above to achieve the accuracy you require.



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