Trigonometric Equations

  • #1

Homework Statement


sin 2θ = sin θ Find the solutions in degrees.


Homework Equations



sin 2θ = 2sinθcosθ

The Attempt at a Solution


sin 2θ = sin θ
2sinθcosθ = sin θ
sinθ *cosθ/sin θ = 1

That's as far as I can get, and I think that is wrong. How do I procede from 2sinθcosθ = sin θ?
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,847
966

Homework Statement


sin 2θ = sin θ Find the solutions in degrees.


Homework Equations



sin 2θ = 2sinθcosθ

The Attempt at a Solution


sin 2θ = sin θ
2sinθcosθ = sin θ
One obvious possibility is [itex]sin(\theta)= 0[/itex]. What values of [itex]\theta[/itex] give that?
IF [itex]sin(\theta)\ne 0[/itex], you can divide by it.

sinθ *cosθ/sin θ = 1
So cancel the [itex]sin(\theta)[/itex]s, giving [itex]cos(\theta)= 1[/math]. What values of [itex]\theta[/itex] give that?

That's as far as I can get, and I think that is wrong. How do I procede from 2sinθcosθ = sin θ?
 
  • #3
Therefore the answer would be 0 degrees and 180 degrees? The book states that answers must greater or equal to one and less than 360.
 

Related Threads on Trigonometric Equations

  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
9
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
5
Views
2K
  • Last Post
2
Replies
42
Views
4K
  • Last Post
Replies
2
Views
944
  • Last Post
Replies
5
Views
985
Top