 My Math Forum Direct method to solve for x in (cos x)/x=0.25
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 April 12th, 2017, 09:22 PM #1 Member   Joined: Nov 2016 From: USA Posts: 36 Thanks: 1 Direct method to solve for x in (cos x)/x=0.25 I can plug in numbers for x and then get closer & closer approximations. What is a quick, direct method to solve for x in: (cos x)/x = 0.25 April 12th, 2017, 09:35 PM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,553 Thanks: 1403 There's no closed form answer. You have to find a numeric solution. You can use Newton's method $f(x) = \dfrac{\cos(x)}{x}-0.25$ $f^\prime(x) = \dfrac{-x\sin(x) -\cos(x)}{x^2}$ $x_{n+1} = x_n - \dfrac{f(x_n)}{f^\prime(x_n)}$ and run this until it converges close enough for your satisfaction I get $x=1.25235$ Thanks from Seventy7 Last edited by romsek; April 12th, 2017 at 10:21 PM. April 12th, 2017, 10:03 PM #3 Senior Member   Joined: May 2016 From: USA Posts: 1,310 Thanks: 551 Umm, for Newton's Method $f(x) = \dfrac{\cos(x)}{x} - 0.25?$ Thanks from romsek Last edited by skipjack; April 13th, 2017 at 03:00 PM. April 13th, 2017, 10:19 AM   #4
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Quote:
 Originally Posted by JeffM1 Umm, for Newton's Method $f(x) = \dfrac{\cos(x)}{x} - 0.25?$
Yes, Newton's method applies to equations of the form f(x) = 0. Here the problem was to solve $\dfrac{\cos(x)}{x}= 0.25$ which is the same as $\dfrac{\cos(x)}{x}- 0.25= 0$.

Last edited by skipjack; April 13th, 2017 at 02:59 PM. April 13th, 2017, 04:09 PM   #5
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Quote:
 Originally Posted by Country Boy Yes, Newton's method applies to equations of the form f(x) = 0. Here the problem was to solve $\dfrac{\cos(x)}{x}= 0.25$ which is the same as $\dfrac{\cos(x)}{x}- 0.25= 0$.
Romsek missed the 0.25 in his original post, but edited it in after JeffM1 pointed it out . Tags cos, direct, method, solve, x or x025 Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Indigo28 Algebra 4 January 13th, 2017 01:20 PM KaiL Calculus 1 September 26th, 2015 01:13 PM knhrawahi Calculus 3 April 19th, 2013 05:13 AM chapsticks Calculus 2 February 21st, 2012 07:58 PM jakeward123 Calculus 5 March 21st, 2011 01:33 PM

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