# Thread: Estimation

1. ## Estimation

Hi,

z= cos(x) sin(x) , x <= |0.1|

I want to estimate z

I know that |z| <= |1| , but is there is a more accurate estimation ?

thx

2. Hello.

Originally Posted by Musab
Hi,

z= cos(x) sin(x) , x <= |0.1|

I want to estimate z

I know that |z| <= 1 , but is there is a more accurate estimation ?

thx
What exactly are you asking for?

z is continious on x <= |0.1|, you can say something about slope and it has the sin-symmetry. And you know z(0) = 0; there are no zeros except for x=0 on your interval...

Yours
Rapha

3. Originally Posted by Musab
Hi,

z= cos(x) sin(x) , x <= |0.1|

I want to estimate z

I know that |z| <= 1 , but is there is a more accurate estimation ?
To a first approximation, z = x. If you want something more accurate, the next approximations are $z = x-\tfrac23x^3$ and $z = x-\tfrac23x^3 + \tfrac2{15}x^5$.

4. I think I haven't explained what I want properly.

|z| <= | n | where n is a number

I want to know the smallest possible value of |n| , so that the accuracy of the approximation rises.

thx

5. is this right :

|z|<= |cos(0) sin(0.1) | ??

6. z dose not equal 1 it is impossible cuz

sinx cosx=sin2x/2 and the largest value of this is 1/2