Help with uncertainty percentage

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To determine the percent uncertainty in theta and sin theta when theta is 20.0 ± 0.5 degrees, the percent uncertainty is calculated as the ratio of the uncertainty to the measured value. The calculation for theta yields a percent uncertainty of 5% using the formula (20.5 - 19.5) / 20 * 100. For sin theta, the approach involves finding the average of sin(20.5) and sin(19.5), then applying the same uncertainty formula. The discussion highlights confusion around applying these calculations correctly. Clear steps and examples are essential for accurate determination of percent uncertainty in both theta and sin theta.
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Homework Statement



Determine the percent uncertainty in theta and in sin theta when theta equals 20.0 + or - 0.5 degrees?
delta theta/theta = ?
delta sin theta/ sin theta = ?

Homework Equations



Percent uncertainty is a ratio of the uncertainty to the measured value.
%uncertainty = uncertainty/measured


The Attempt at a Solution



I'm not sure exactly how to solve it. I know that in some cases you would find each deviation, average the two values, and then divide the difference between the average and one deviation by the average. I'm just not sure how to apply that to this problem.

theta 1 = 20.5
theta 2 = 19.5
theta average = 20
 
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Is it the difference between max and min values, divided by average, multiplied by 100?
(20.5-19.5)/20*100= 5%
and sin(20.5)-sin(19.5)/((sin20.5 + sin19.5)/2)*100
 
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