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From: Fred Nurk on 6 Jul 2010 20:29 If z = sin(x) and sin(1) = a then, using the first order approximation, the value of sin(1.1) is equal to: A 0.1(1 - a ^ 2) ^ (1 / 2) B 0.1cos(1) C 0.1(1 - a ^ 2) ^ (1 / 2) + a D a + 0.1 E 0.1a Here's my working out and what I got up to: sin(1 + 1 / 10) approximately = sin(1) + (1 / 10)f'(1) approximately = a + (1 / 10)f'(1) d(sin(x)) / dx = cos(x) cos(1) = From here, I can say that C is the only answer given that could be right. But is it impossible to write cos(1) in terms of a and/or z? Am I able to show that sin(1.1) is C? TIA, Fred
From: Francois Grieu on 7 Jul 2010 02:02 Le 07/07/2010 02:29, Fred Nurk a écrit : > If z = sin(x) and sin(1) = a then, using the first order approximation, > the value of sin(1.1) is equal to: > > A 0.1(1 - a ^ 2) ^ (1 / 2) > B 0.1cos(1) > C 0.1(1 - a ^ 2) ^ (1 / 2) + a > D a + 0.1 > E 0.1a > > Here's my working out and what I got up to: > sin(1 + 1 / 10) approximately = sin(1) + (1 / 10)f'(1) > approximately = a + (1 / 10)f'(1) > d(sin(x)) / dx = cos(x) > cos(1) = > > From here, I can say that C is the only answer given that could be right. > But is it impossible to write cos(1) in terms of a and/or z? Am I able to > show that sin(1.1) is C? Hint: sin(a)^2 + cos(a)^2 = 1. Check the sign of sin(a). Francois Grieu
From: Francois Grieu on 7 Jul 2010 03:08 Le 07/07/2010 02:29, Fred Nurk a écrit : > If z = sin(x) and sin(1) = a then, using the first order approximation, > the value of sin(1.1) is equal to: > > A 0.1(1 - a ^ 2) ^ (1 / 2) > B 0.1cos(1) > C 0.1(1 - a ^ 2) ^ (1 / 2) + a > D a + 0.1 > E 0.1a > > Here's my working out and what I got up to: > sin(1 + 1 / 10) approximately = sin(1) + (1 / 10)f'(1) > approximately = a + (1 / 10)f'(1) > d(sin(x)) / dx = cos(x) > cos(1) = > > From here, I can say that C is the only answer given that could be right. > But is it impossible to write cos(1) in terms of a and/or z? Am I able to > show that sin(1.1) is C? Hint: sin(1)^2 + cos(1)^2 = 1. Check the sign of cos(1). Francois Grieu [reposted with correction]
From: Fred Nurk on 7 Jul 2010 05:00 Francois Grieu wrote: > <snip> > Hint: sin(1)^2 + cos(1)^2 = 1. Right. cos(1) = {1 - [sin(1)] ^ 2} ^ (1 / 2) = (1 - a ^ 2) ^ (1 / 2) > Check the sign of cos(1). Why? It is now clear that the answer is C. > <snip> TIA, Fred
From: Francois Grieu on 7 Jul 2010 06:21
Fred Nurk wrote: > If z = sin(x) and sin(1) = a then, using the first > order approximation, the value of sin(1.1) is equal to: > > A 0.1(1 - a ^ 2) ^ (1 / 2) > B 0.1cos(1) > C 0.1(1 - a ^ 2) ^ (1 / 2) + a > D a + 0.1 > E 0.1a > Francois Grieu wrote: >> Hint: sin(1)^2 + cos(1)^2 = 1. > Right. cos(1) = {1 - [sin(1)] ^ 2} ^ (1 / 2) > = (1 - a ^ 2) ^ (1 / 2) > >> Check the sign of cos(1). > Why? It is now clear that the answer is C. Because on the problem If z = sin(x) and sin(2) = a then, using the first order approximation, the value of sin(2.1) is equal to: A 0.1(1 - a ^ 2) ^ (1 / 2) B 0.1cos(2) C 0.1(1 - a ^ 2) ^ (1 / 2) + a D a + 0.1 E 0.1a the right answer would be: neither of the above, due to a sign issue. Note: in the schooling system I practiced, there was no multiple choices tests, one had to give the reasoning, and would not get the highest mark without stating all relevant hypothesis used. Francois Grieu |