Error Propigation Cosine
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About About Answers Community Guidelines Leaderboard Knowledge Partners Points & Levels Blog Safety Tips Science & Mathematics Physics Next Error propagation of sine? For my physics lab class. Find sin(theta), theta=.31 + or - .01 radians. What will the error be? 1 following 3 answers 3 Report Abuse Are you sure you want to delete this answer? error propagation calculator Yes No Sorry, something has gone wrong. Trending Now Erykah Badu Tom Cruise Samsung Note7s Adrien Broner Faith Hill Car Insurance Kylie Jenner Contact Lenses Great Lakes Personal Loans Answers Relevance Rating Newest Oldest Best Answer: You can do it explicitly. Leaving out units for neatness and not worrying about significant figures: sin(0.31+0.01) = sin(0.32) = 0.3146 sin(0.31) =0.3051 sin(0.31-0.01) = sin(0.30) = 0.2955 So to a reasonable approximation, the error is +/- (0.3146-0.2955)/2 = +/- 0.00955 This is a percentage error of 100 x 0.00955/0.3051 = 3.1% The formal method is: y = sin(x) dy/dx = cos(x) Δy = (dy/dx)Δx = (cos(x))Δx So if x =0.31 and Δx =0.01, Δy =cos(0.31) * 0.01 = 0.00952 You might find the link useful. Source(s): http://www.rit.edu/cos/uphysics/uncertai... Steve4Physics · 5 years ago 2 Thumbs up 2 Thumbs down Comment Add a comment Submit · just now Asker's rating Report Abuse Error Propagation Formula Source(s): https://shrink.im/a0c3h casstevens · 1 week ago 0 Thumbs up 1 Thumbs down Comment Add a c
uncertainty of an answer obtained from a calculation. Every time data are measured, there is an uncertainty associated with that measurement. (Refer to guide to Measurement and Uncertainty.)
Sine Cosine Error Metrology
If these measurements used in your calculation have some uncertainty associated with
Error Propagation Square Root
them, then the final answer will, of course, have some level of uncertainty. For instance, in lab you might uncertainty of sine measure an object's position at different times in order to find the object's average velocity. Since both distance and time measurements have uncertainties associated with them, those uncertainties follow the numbers https://answers.yahoo.com/question/index?qid=20110926115447AAxjvqN throughout the calculations and eventually affect your final answer for the velocity of that object. How would you determine the uncertainty in your calculated values? In lab, graphs are often used where LoggerPro software calculates uncertainties in slope and intercept values for you. In other classes, like chemistry, there are particular ways to calculate uncertainties. In fact, since uncertainty calculations are based http://physics.appstate.edu/undergraduate-programs/laboratory/resources/error-propagation on statistics, there are as many different ways to determine uncertainties as there are statistical methods. The error propagation methods presented in this guide are a set of general rules that will be consistently used for all levels of physics classes in this department. In the following examples: q is the result of a mathematical operation δ is the uncertainty associated with a measurement. For example, if you have a measurement that looks like this: m = 20.4 kg ±0.2 kg Thenq = 20.4 kg and δm = 0.2 kg First Step: Make sure that your units are consistent Make sure that you are using SI units and that they are consistent. If you are converting between unit systems, then you are probably multiplying your value by a constant. Please see the following rule on how to use constants. Logger Pro If you are using a curve fit generated by Logger Pro, please use the uncertainty associated with the parameters that Logger Pro give you. In the above linear fit, m = 0.9000 andδm = 0.05774. The uncertainty should be rounded to 0.06, whi
a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn http://physics.stackexchange.com/questions/94110/error-propagation-estimations-for-sine-and-cosine more about Stack Overflow the company Business Learn more about hiring developers or posting ads with us Physics Questions Tags Users Badges Unanswered Ask Question _ Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The error propagation best answers are voted up and rise to the top Error propagation estimations for sine and cosine up vote 0 down vote favorite My lab manual gives this: $B$ is a function of $A$, Greek are uncertainties... $$B + \beta = \sin(A + \alpha) = \sin(A)\cdot\cos(\alpha) + \sin(\alpha)\cdot\cos(A)$$ --> because $\alpha$ is taken to be (at least relatively) small, $\cos(\alpha) \to 1$, and $\sin(\alpha) \to \alpha$, error propigation cosine measured in radians. I see that $\cos(\alpha) \to 1$, but I would have expected that $\sin(\alpha)$ for a small would, by the same logic, go to 0. Has it got something to do with the rate of change of either function near zero? Why is $\cos(\alpha)$ of small $\alpha$ not also proportional or written by relation to $\alpha$? experimental-technique error-analysis calculus share|cite|improve this question edited Jan 17 '14 at 17:15 Kyle Kanos 18.8k103874 asked Jan 17 '14 at 16:22 user37464 684 1 Have a look at Taylor series. Normally you have to keep at least the linear term to have consistent results. –DarioP Jan 17 '14 at 16:33 add a comment| 3 Answers 3 active oldest votes up vote 1 down vote accepted The easiest way is to plot $x$, $\sin(x)$, and $\cos(x)$. Fortunately, Wikipedia has done that for us: From the first graph, when $x\lesssim0.2$ rad, $\sin(x)\simeq x$. From the second graph, the approximation that $\cos(x)\simeq1$ really only holds when $x\lesssim0.1$ rad; normally one writes it as $\cos(x)\approx1-x^2/2$. The reason for these approximations come from their series expansion: $$\sin(x)=x-\frac16x^3+\frac{1}{120}x^5+\cdots\\ \cos(x)=1-\frac12x^2+\frac{1}{24}x^4+\cdots $$ when $x$ is small, $x^3\approx0$, and all other higher terms are also
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