May god help me (1 Viewer)

[fullonoob]

Approximate the difference between cosx and 1 - .5x^2 for small angles, and find the smallest angle, in degrees, for which this difference exceeds 0.001. DO NOT USE CALCULATOR i.e. show it
EXTRA INFO :: cos x .=. 1 - .5x^2

Trebla plox

 

[Trebla]

Use cos x ~ 1 for small x then solve x²/2 = 0.001

 

[fullonoob]

cos x ~ 1 - .5x^2
find x for which this difference exceeds 0.001. show me algebraically

 

[Lukybear]

as x>>0
cosx>1
RHS>1
thus RHS=LHS as x>0

 

[fullonoob]

lol??? find the smallest angle, in degrees, for which this difference exceeds 0.001.

 

[shaon0]

lol??? find the smallest angle, in degrees, for which this difference exceeds 0.001.

cos(x)=1-x^2/2!+x^4/4!+...=Sigma {k=0,n} (-1)^k.(x^(2k))/(2k)!
So what they are asking is find:
Sigma {k=2,n) (-1)^k.(x^(2k))/(2k)!>0.001, ie find the error in using cos(x)=1-x^2/2 opposed to the sum stated above.
But, common sense dictates the answer is x=0 for f(x)=cos(x)-1+x^2/2=0.
So for, f>0, x is small ie x=:sqrt(0.002).
Also, you could probs use Newton's method of approximation where g=cos(x)+x^2/2-1.001 but be careful of turning pts.

 

[harrisony]

cos(x)=1-x^2/2!+x^4/4!+...=Sigma {k=0,n} (-1)^k.(x^(2k))/(2k)!
So what they are asking is find:
Sigma {k=2,n) (-1)^k.(x^(2k))/(2k)!>0.001, ie find the error in using cos(x)=1-x^2/2 opposed to the sum stated above.
But, common sense dictates the answer is x=0 for f(x)=cos(x)-1+x^2/2=0.
So for, f>0, x is small ie x=:sqrt(0.002).
Also, you could probs use Newton's method of approximation where g=cos(x)+x^2/2-1.001 but be careful of turning pts.

 

[ohexploitable]

Too much effort!

 

[shaon0]

No, but thanks anyway for the suggestion lol

 

[fullonoob]

shaono dont have friend lol jooking xD
if you can make him use latex ill call you god, never seen him use latex before
ill be happy if you show me full working out, and actually show answer as well, then ill read it

 

[shaon0]

shaono dont have friend lol jooking xD
if you can make him use latex ill call you god, never seen him use latex before
ill be happy if you show me full working out, and actually show answer as well, then ill read it

I don't understand ur 1st sentence lol. In regards to q, it's pretty useless, i would just get over it and do other q's.