Confusion with very basic algebra

  • #1
quasar987
Science Advisor
Homework Helper
Gold Member
4,796
32
I'm trying to find the points t in (0,2[itex]\pi[/itex]) such that sint=sin4t. So I use the fact that sinA=sinB <==> A=B+2n[itex]\pi[/itex] ([itex]n\in\mathbb{Z}[/itex]), which yields t=2n[itex]\pi[/itex]/3 ([itex]n\in\mathbb{Z}[/itex]). The only solutions of this in (0,2[itex]\pi[/itex]) are 2[itex]\pi[/itex]/3 and 4[itex]\pi[/itex]/3.

However, there are 7 intersection points, says the "indirect method" of finding the zeros in (0,2[itex]\pi[/itex]) of sint-sin4t = sint+sin(-4t) =2sin(3t/2)cos(5t/2).

The number 7 is also confirmed by my calculator. So why doesn't the direct method using only the properties of sine, give the correct answer?? :confused:
 
Last edited:
Mathematics news on Phys.org
  • #2
sinA=sinB <=> A=B+2npi or A=(2n+1)pi-B. Remember that sin(x) is periodic with period 2pi, but not one-to-one on a given period (ie, there are points within a single period with the same sin).
 
  • #3
Hey, you're right! Thanks StatusX.
 

Similar threads

Replies
1
Views
1K
3
Replies
80
Views
7K
Replies
8
Views
2K
2
Replies
61
Views
8K
Replies
25
Views
3K
3
Replies
100
Views
9K
Back
Top