By calculating a Taylor approximation, determine K

Answers and Replies

  • #2
Charles Link
Homework Helper
Insights Author
Gold Member
2020 Award
4,890
2,199
I recommend you first expand this function using ## \sin(\theta-\phi)=\sin(\theta) \cos(\phi)-\sin(\phi) \cos(\theta) ##, and then work a Taylor series after putting in the values for ## \theta ## and ## \phi ##.
 
  • #3
Charles Link
Homework Helper
Insights Author
Gold Member
2020 Award
4,890
2,199
Assuming you did the above step, what do you get for the Taylor expansion of ## \cos(\frac{\pi}{2} x) ##?
 
  • #4
Charles Link
Homework Helper
Insights Author
Gold Member
2020 Award
4,890
2,199
I'm going to give you a couple more hints on this problem, because it is really quite a neat one: ## \\ ## Let ## f(x)=\cos(\frac{\pi}{2}x )##. This can be written as ## f(x)=\cos(bx) ## where ## b=\frac{\pi}{2} ##. Now, by the chain rule, ## f'(x)=-b \sin(bx) ##, and ## f''(x)=-b^2 \cos(bx) ##. The Taylor series ## f(x)=f(0)+f'(0)(x-0)+f''(0) \frac{(x-0)^2}{2!}+... ## ## \\ ## I gave you a couple of the terms here to get you started, but this problem actually will require even the 4th derivative. (Compute these first couple of terms and you will see why).
 

Related Threads on By calculating a Taylor approximation, determine K

  • Last Post
Replies
2
Views
660
  • Last Post
Replies
5
Views
702
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
8
Views
2K
Replies
12
Views
2K
Top