Chapter 1 55. The trigonometric function is not a linear function of the angle, so we can find the uncertainty in the sine by calculating two values. ( a ) Percent uncertainty in θ = (0.5°/15.0°) 100 = 3% . We find the percent uncertainty in the sine from sin 15.0° = 0.2588; sin 15.5° = 0.2672; Percent uncertainty in sin = [(0.2672 – 0.2588)/0.2588] 100 = 3% . ( b ) Percent uncertainty in = (0.5°/75.0°) 100 = 0.7% . We find the percent uncertainty in the sine from sin 75.0° = 0.9659; sin 75.5° = 0.9681; Percent uncertainty in sin = [(0.9681 – 0.9659)/0.9659] 100 = 0.2% . Note that it is possible to approximate uncertainties with differential quantities, if the angle is not very small (i. e.,
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This note was uploaded on 03/08/2010 for the course PHY 7A taught by Professor Zettl during the Fall '08 term at Berkeley.