Pre-Calculus

posted by Sara

For what values of x is it true that |sin(x)-x| < 0.01?

1. bobpursley

I have spend 20 min on this,with no results. I went the Taylor expansion of sin(x), and it didn't help. When you get a solution, please post it. FYI, I graphed it, and was surprised. It reminded me how accurate the small angle approximation is.

2. Reiny

I looked at the solution to
|sinx -x| = .01 and using Newton's Method found
x = ±.392493378

then testing, I found the above to be true for

-.3925 < x < + .3924

(for sinx - x = .01 my iteration expression was
(xcosx - sinx + .01)/(cosx - 1) )

Similar Questions

1. Calculus

Consider the function f(x)=sin(1/x) Find a sequence of x-values that approach 0 such that sin (1/x)=0 sin (1/x)=1 sin (1/x)=-1 Is sin sin (1/x)=0 and sin (1/x)=-1 does not exist. What is sin (1/x)=1 then. How would I show the sequence …
2. Calculus

Consider the function f(x)=sin(1/x) Find a sequence of x-values that approach 0 such that sin (1/x)=0 sin (1/x)=1 sin (1/x)=-1 Is sin sin (1/x)=0 and sin (1/x)=-1 does not exist. What is sin (1/x)=1 then.
3. Calculus

Consider the function f(x)=sin(1/x) Find a sequence of x-values that approach 0 such that (1) sin (1/x)=0 {Hint: Use the fact that sin(pi) = sin(2pi)=sin(3pi)=...=sin(npi)=0} (2) sin (1/x)=1 {Hint: Use the fact that sin(npi)/2)=1 if …
4. Calculus

Consider the function f(x)=sin(1/x) Find a sequence of x-values that approach 0 such that (1) sin (1/x)=0 {Hint: Use the fact that sin(pi) = sin(2pi)=sin(3pi)=...=sin(npi)=0} (2) sin (1/x)=1 {Hint: Use the fact that sin(npi)/2)=1 if …
5. Pre-Calculus

How do I solve: sin theta = -1 for all real values of theta?
6. Pre-calculus

Does Sin^-1(-x)=-Sinx? Is it true or false and explain.
7. Public High School Pre Calculus HH

Ok I do not know how to do this problem. I know that csc is simply sin^-1 sin (- pi/12) csc ( (37 pi)/12 ok now I know this also sin (- pi /12 ) = - sin ( pi/12) not really sure how that helps I don't know were to go from here ( - …
8. Pre Calculus

Pre Calculus why is sin(-20)/cos 380 equal to tan (-200)
9. calculus

Determine all the absolute extreme values for the function f(x,y) = sin(x)*sin(y)*sin(x+y)on the square 0<x<pi, 0<y<pi
10. Pre-calculus

If sin x=-3/5 and sec x>0, find all the other circular function values of x

More Similar Questions