# What is the largest possible error in the component?

[SOLVED] Error Calculation

## Homework Statement

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?

## 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?

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.)