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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: xkcirtap on November 10, 2011, 07:38:17 pm

Title: Euler's Question Problem causing... problems :/
Post by: xkcirtap on November 10, 2011, 07:38:17 pm: Hey there; I've been stumped on this question for awhile now; I can't seem to get the answer:

Let dy/dx = 2 arcsin (x-1) and (x0, y0) = (0,1).
Using Euler's method, with a step size of 0.2, the value of y2 would be given by...?

I get the method but for some reason I'm not getting the desired answer provided in the multiple choice. Help would be much appreciated! :)
Title: Re: Euler's Question Problem causing... problems :/
Post by: Vincezor on November 10, 2011, 07:45:08 pm: y1 = 1 + 0.2*arcsin(-1)

y2 = (1+0.2*arcsin(-1)) + 0.2*arcsin(0.2-1)

$y_2 \approx 0.5004$

Is this the correct answer? :S
Title: Re: Euler's Question Problem causing... problems :/
Post by: xkcirtap on November 10, 2011, 07:47:13 pm: Not too sure; the multiple choice answers given are in exact numbers. If you like; I'll type up the choices? or the exact form of the answer?
Title: Re: Euler's Question Problem causing... problems :/
Post by: Vincezor on November 10, 2011, 07:52:51 pm: $1-\frac{\pi}{10}-\frac{sin^{-1}(4/5)}{5}$

is what I get on my CAS...
Title: Re: Euler's Question Problem causing... problems :/
Post by: xkcirtap on November 10, 2011, 07:56:09 pm: It's pretty close unless I'm looking at your answer wrong: The answer is 1-(pi/5) - 0.4arcsin(0.8) :(
Title: Re: Euler's Question Problem causing... problems :/
Post by: xkcirtap on November 10, 2011, 07:59:24 pm: er that's a arcsin(0.8 ) at the end... emoticons :@
Title: Re: Euler's Question Problem causing... problems :/
Post by: jaz_rocks_123 on November 10, 2011, 08:17:52 pm: What's wrong with that answer?

step 1:

1+2/5*arcsin(-1)
=1-pi/5

Step 2:
1-pi/5+2*0.2*arcsin(0.2-1)
=1-pi/5-0.4arcsin(0.8 )
Title: Re: Euler's Question Problem causing... problems :/
Post by: xkcirtap on November 10, 2011, 08:23:35 pm: Nothing; but whilst working out; I couldn't get exact values on my calculator and hence had no idea how to even get that number. I think it has something to do with the fact that I'm typing in 'csc(x)' for arcsin... Still, thanks for showing that step by step process :)

Edit: Just realised csc wasn't arcsin == However, even when typing in arcsin; I get a decimal not an exact number.

Edit (2): Okay figured it now; it was because I keep writing 0.4; I tried 2/5 and it works. Thanks Jaz!
Title: Re: Euler's Question Problem causing... problems :/
Post by: Andiio on November 10, 2011, 08:58:05 pm: Quote from: xkcirtap on November 10, 2011, 08:23:35 pm
Nothing; but whilst working out; I couldn't get exact values on my calculator and hence had no idea how to even get that number. I think it has something to do with the fact that I'm typing in 'csc(x)' for arcsin... Still, thanks for showing that step by step process :)

Edit: Just realised csc wasn't arcsin == However, even when typing in arcsin; I get a decimal not an exact number.

Edit (2): Okay figured it now; it was because I keep writing 0.4; I tried 2/5 and it works. Thanks Jaz!

Which calc are you using?
Title: Re: Euler's Question Problem causing... problems :/
Post by: abeybaby on November 10, 2011, 08:59:58 pm: Even if you get decimals its fine, just plug all the choices into your calc and see which ones match up