Trig Equation

  • Thread starter cscott
  • Start date
  • #26
TD
Homework Helper
1,022
0
cscott said:
Wait! Let me just check my understanding: the solution to the equation I posted can be either the one including pi/3 or the one inlcluding 4pi/3 and each solution has to encorporate the negative and positive sqrt(3)/2?

I say this because pi/3 + pi gives -sqrt(3)/2 but I got the pi/3 in the first place using sin x = +sqrt(3)/2

Is this correct? It doesn't seem like it...
From the positive root, the solution pi/3 and its complementary solution pi-pi/3 = 2pi/3 follow.
From the negative root, the solution -pi/3 (or 5pi/3) and its complementary solution 4pi/3 follow.

You see?
 
  • #27
782
1
TD said:
From the positive root, the solution pi/3 and its complementary solution pi-pi/3 = 2pi/3 follow.
From the negative root, the solution -pi/3 (or 5pi/3) and its complementary solution 4pi/3 follow.

You see?

I understand that there is two solutions for each root but I don't see how that translates into the one solution per root. How do you get 2pi/3 from pi/3 + pi * k? Shouldn't I be able to put any integral value for "k" and get a positive sqrt(3)/2 answer in that case?
 
Last edited:
  • #28
TD
Homework Helper
1,022
0
For the positive root, we had: pi/3 and 2pi/3
For the negative root, we had: 4pi/3 and 5pi/3

Of course, all +2k*pi.

But now notice that 4pi/3 = pi/3 + pi and 5pi/3 = 2pi/3 + pi.
So you need to 'cross' the solutions of both roots, take them all together.
Then you can leave out the two redundant ones and use +k*pi instead of +2k*pi.
 
  • #29
782
1
I get it! I get it! Thanks again for being patient with me.

It's like this was a one on one (fast posts) :tongue:
 
  • #30
TD
Homework Helper
1,022
0
No problem, glad you understand :smile:
 

Related Threads on Trig Equation

  • Last Post
Replies
15
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
19
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
10
Views
857
Top