Trig Equation

  • Thread starter Moose352
  • Start date
  • #1
166
0

Main Question or Discussion Point

For some reason, I seem to be unable to algebraically solve this equation:

sin(x) + sqrt(3)cos(x) = 1

Any help would be appreciated.
 

Answers and Replies

  • #2
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
14,916
17
You need to combnie the LHS into a single trig function.
 
  • #3
166
0
Never mind, LHS means left hand side.

Yes, I know I need to convert the left side into the same trig function. That is what I'm having trouble with.
 
  • #4
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
14,916
17
All righty.

Suppose the equation was of the form:

[tex]
\cos \frac{\pi}{5} \sin x + \sin \frac{\pi}{5} \cos x = 1
[/tex]

Would you be able to solve for x?
 
  • #5
166
0
Yes, but I don't know how exactly that is applied here.
 
  • #6
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
14,916
17
(I should've mentioned that there will be a couple steps to this)


Ok. pretend for a moment that you could solve the equations:

cos y = 1
sin y = √3

Then would you be able to solve the equation:

sin x + √3 cos x = 1
 
  • #7
matt grime
Science Advisor
Homework Helper
9,395
3
There is a general formula for this, usuallr referred to as rsin(theta + x)

but here, have you thought about multiplying everything by the same number so you get something akin to Hurkyl's example (think of some obvious values of cos sin etc involving sqrt(3))?
 
  • #8
166
0
I'm sorry, but still nope :(
 
  • #9
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
14,916
17
So you know how to solve the equation:

cos y sin x + sin y cos x = z

for x, if you know what y and z are.


Now, if I want to solve the equation

A sin x + B cos x = z

and I know that

A = cos y
and
B = sin y

Then can you solve this equation for x?
 
  • #10
166
0
Hmm, I think I figured it out. Tell me if I am right:

cos(y) = z
sin(y) = z*sqrt(3)

So y = tan^-1(sqrt(3)) = pi/3

So

sin(x)cos(y) - cos(x)sin(y) = 1z
sin(x-y) = 1z
x-y = sin^-1(.5)

and then solve for x?

Thanks a lot
 
  • #11
166
0
is there any significance to the value z (in my previous post) always seeming to equal 1/sqrt(A^2 + B^2)?
 
  • #12
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
14,916
17
Well, what does [itex]\sin^2 x + \cos^2 x[/itex] equal?
 
  • #13
166
0
That makes sense! I can't beleive I didn't figure this problem out myself.

Thanks a lot for the help.
 

Related Threads for: Trig Equation

  • Last Post
Replies
14
Views
2K
  • Last Post
Replies
8
Views
3K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
13
Views
5K
Replies
3
Views
3K
  • Last Post
Replies
10
Views
795
  • Last Post
Replies
10
Views
3K
  • Last Post
Replies
5
Views
3K
Top