I have two questions regarding uncertainties in measurements.First, if I have some measured value for x with an uncertainty ± e, what would be the uncertainty in sin ⁡ x, ± sin ⁡ e?Then, if I have a range of values from 30 to 46, can I include an uncertainty value of ± 2? Even if it’s not wrong from a mathematical point of view, would it be unsuitable in a physics laboratory report?

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I have two questions regarding uncertainties in measurements.First, if I have some measured value for   x with an uncertainty   ±  e, what would be the uncertainty in   sin  ⁡  x,   ±  sin  ⁡  e?Then, if I have a range of values from 30 to 46, can I include an uncertainty value of   ±  2? Even if it’s not wrong from a mathematical point of view, would it be unsuitable in a physics laboratory report?

antantil0 · Accepted Answer

First: You don&#039;t necessarily get an uncertainty of   sin  ⁡  (  x  )  ±  sin  ⁡  (  e  ). Remember that the sine function is periodic. So if you have that x=0 and   e  =  2  π. Then you would not get an uncertainty of   sin  ⁡  (  0  )  ±  sin  ⁡  (  2  π  )  =  0  ±  0. In such a case you would get   0  ±  1 since on the interval   [  −  2  π  ,  2  π  ] sine takes all values. Now for another example: If you get a value of x=0.7 and e=0.1 then indeed you get   sin  ⁡  (  x  )  ±  sin  ⁡  (  e  ) because sin is strictly increasing on the interval [0.6,0.8].Second: I don&#039;t think I quite understand, and you might want to ask about some of this on the physics.SE site, but if you are trying to measure something, and you get values ranging from 30 to 46, then I guess you might give the average of 38 with an uncertainty of   ±  8. Now, from what I understand, giving uncertainties of measurements in physics is about more than just giving the range of values that you got. You also have to account for uncertainties in the instruments.Edit: If you have   sin  ⁡  (  x  ) and you measure x in degrees, then sin is increasing on the interval [30,46]. So if the uncertainty is ±2 on x (from the instrument or what ever), then the uncertainty on sin(x) is   ±  sin  ⁡  (  2  ).

I have two questions regarding uncertainties in measurements. First, if I have some measured value

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