# Error Calculation

1. Dec 21, 2007

### jesuslovesu

[SOLVED] Error Calculation

1. The problem statement, all variables and given/known data
A force 500nt is measured with a possible error of 1nt.
Its component in a direction 60 deg away from its lnie of action is required. Where the angle is subject to an error of .5 deg. What is the largest possible error in the component?

2. Relevant equations

3. The attempt at a solution
I was thinking 1/500 + .5/60 would bring the percentage and then if I multiply % * 500 I would get the amount of "nt"s (what's an nt, a newton?) however that gives a result that is a little too large. I would imagine my problem lies with the angle.. do I need to do something special with it?

2. Dec 21, 2007

### HallsofIvy

Staff Emeritus
you can't just add the relative error (0.5/60) because it is the sine of the angle, not the angle itself, that is added. If this were not in "precalcus, I woud recommend approxmating the error in the sine by $dy= (\pi/180) cos x dx$. (If y= sin(x) then dy/dx= cos(x) so to a linear approximation, the error in sin(x) is cos(x)dx. The reason for for the $\pi/180$ factor is that x is measured in degrees not radians.)

If you are not familiar with using the derivative to approximate a function, you can do a direct calculation of the maximum error. The largest possible values for the nts measurement (yes, that's "Newtons") is 501 and the largest possible angle is 60.5 degrees. Do the calculation for that. The smallest possible corresponding values are 499 nts and 59.5 degrees do the same calculation for that. Which is those is the largest deviation from the value for 500 nts and 60 degrees? That is the maximum error.