Help with uncertainty percentage

  • Thread starter Thread starter GreenMan39
  • Start date Start date
  • Tags Tags
    Uncertainty
Click For Summary
SUMMARY

The discussion focuses on calculating the percent uncertainty in both theta and sin(theta) for a given angle of 20.0 degrees with an uncertainty of ±0.5 degrees. The calculated percent uncertainty for theta is 5%, derived from the formula (20.5 - 19.5) / 20 * 100. For sin(theta), the approach involves averaging the sine values of the extreme angles, applying the formula for percent uncertainty to determine the deviation from the average sine value.

PREREQUISITES
  • Understanding of percent uncertainty calculations
  • Knowledge of trigonometric functions, specifically sine
  • Familiarity with basic algebraic manipulation
  • Ability to perform calculations involving averages
NEXT STEPS
  • Learn how to calculate percent uncertainty in various scientific measurements
  • Explore the properties of trigonometric functions and their derivatives
  • Study error propagation techniques in experimental physics
  • Investigate the significance of significant figures in measurement
USEFUL FOR

Students in physics or engineering courses, educators teaching measurement and uncertainty, and anyone involved in experimental data analysis.

GreenMan39
Messages
2
Reaction score
0

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
 
Physics news on Phys.org
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
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
4K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 8 ·
Replies
8
Views
2K
Replies
15
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
6
Views
2K
Replies
5
Views
5K
  • · Replies 6 ·
Replies
6
Views
5K