• Support PF! Buy your school textbooks, materials and every day products Here!

Angle Help!15 = arctan(2/x) - arctan (1/x)

  • Thread starter Pawnag3
  • Start date
  • #1
12
0

Homework Statement


Basically, solve for x
15 = arctan(2/x) - arctan (1/x)

Homework Equations


tan (A-B) = (Tan A -Tan B) / (1+Tan A*Tan B)

The Attempt at a Solution


I really tried everything.
My first step was to:
Let y = arctan (2/x)
Therefore, tan y = 2/x
Similarly, u = 1/x
Then, tan (y-u) = (Tan y -Tan u) / (1+Tan u*Tan y) = 15
15 = (2/x-(1/x) / (1+(2/x^2)
15 = (1/x) / (x^2 + 2 / x^2)
15 = (x) / (x^2+2)
15x^2 + 30 - x = 0
Which has no real roots :(
But, with guess and check, it's around 0.65
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
6,230
31
You need to post an attempt before we can help you. Start by taking the tangent of both sides.
 
  • #3
12
0
Yeah, sorry. I just misclicked the first time
 
  • #4
12
0
Alright, sorry guys to waste your time, but I believe I figured it out. Thanks for the hint of "tanning" both sides.
Instead of 15, it's supposed to be tan 15.
So that,
x/(x^2+2) = tan 15
x = 0.64
x = 3.08 (approximately)

Thanks for the help!
 
  • #5
Mentallic
Homework Helper
3,798
94
If you rearrange that equation you'll get the quadratic

[tex]x^2-\frac{1}{tan(15)}x+2=0[/tex]

There are no real solutions to this quadratic.
 

Related Threads on Angle Help!15 = arctan(2/x) - arctan (1/x)

  • Last Post
Replies
4
Views
3K
Replies
2
Views
82K
  • Last Post
Replies
1
Views
11K
Replies
2
Views
2K
  • Last Post
Replies
2
Views
4K
  • Last Post
Replies
3
Views
4K
  • Last Post
Replies
2
Views
4K
  • Last Post
Replies
7
Views
3K
  • Last Post
Replies
10
Views
2K
  • Last Post
Replies
6
Views
566
Top