Error Propagation Sine Cosine
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here for 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 more about Stack Overflow the company Business Learn more about hiring developers or posting ads with us Mathematics Questions Tags Users Badges Unanswered Ask Question _ Mathematics Stack Exchange is a question and answer site for people studying math https://answers.yahoo.com/question/index?qid=20110926115447AAxjvqN at any level and professionals in related fields. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top Calculate uncertainty of sine function result up vote 1 down vote favorite 1 http://math.stackexchange.com/questions/1045076/calculate-uncertainty-of-sine-function-result I have an angle given in degrees: $$\theta_{\min} = 63^{\circ} \pm 0.5^{\circ}$$ I need to calculate it's sine and still know the uncertainty of the value: $$n = 2\sin(\theta_{\min}) = 1.7820130483767356 \pm ???$$ How do I calculate the value represented by ???? Edit: I cheated and had a look in my friends work. This is how he did it: $$u_C=\sqrt{\left(\dfrac{\partial n}{\partial \theta_\min}u_C(\theta_\min)\right)^2}=\sqrt{\left(2\cos63^\circ\cdot\dfrac{0.5^\circ}{\sqrt{12}}\right)^2}=\sqrt{(0.908\cdot0.144)^2}=0.131$$ But I don't seem to understand that, though I encountered similar thing before. trigonometry error-propagation share|cite|improve this question edited Nov 30 '14 at 15:22 Mathematician171 2,813829 asked Nov 30 '14 at 14:59 Tomáš Zato 184212 add a comment| 3 Answers 3 active oldest votes up vote 2 down vote accepted Let's write your stuff in a cleaner way: $$n_\text{avg} = 2\sin(63°) = 1.7820130483767356$$ $$n = n_\text{avg} \pm^{u}_l \ .$$ Then $$u = 2\sin(63.5°) - 2\sin(63°)$$ $$l = 2\sin(63°) - 2\sin(62.5°)$$ The way your friend does it is via first order Taylor approximation: $$\Delta n \approx \left.\frac{dn}{d\theta}\right|_{\theta=\theta_\t
here for 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://math.stackexchange.com/questions/963803/relative-error-of-cos-and-sin-functions more about Stack Overflow the company Business Learn more about hiring developers or posting ads with us Mathematics Questions Tags Users Badges Unanswered Ask Question _ Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer error propagation The best answers are voted up and rise to the top Relative error % of cos and sin functions? up vote 0 down vote favorite I've been searching all over the net and I can't seem to find a definitive answer - perhaps I'm asking the wrong question. How does one calculate the relative error (%) of the cos/sin/tan of an angle in degrees? So, let's say error propagation sine that I have an angle of 30 degrees with an absolute error of ±2. The absolute error of the sin of 30 degrees would be: $sin (30+2)-sin(30) = 0.0299 $ Now what do I do to obtain the relative error? error-propagation share|cite|improve this question asked Oct 8 '14 at 14:20 Ursa Major 173212 Relative error is absolute error divided by function value. –Arthur Oct 8 '14 at 14:22 add a comment| 1 Answer 1 active oldest votes up vote 1 down vote accepted By definition relative error is given by $\delta f / f$ so f here is sin30 and the numerator is the difference you have written in your question. To calculate percentage error just multiply relative error by 100. share|cite|improve this answer answered Oct 8 '14 at 14:27 Jasser 1,523418 add a comment| Your Answer draft saved draft discarded Sign up or log in Sign up using Google Sign up using Facebook Sign up using Email and Password Post as a guest Name Email Post as a guest Name Email discard By posting your answer, you agree to the privacy policy and terms of service. Not the answer you're looking for? Browse other questions tagged error-prop
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