1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Solving Trig Equations In A Given Range

  1. Nov 7, 2013 #1
    1. The problem statement, all variables and given/known data

    Solve cos(3θ) = 0.85 in the range 0 ≤ θ ≤ 360°

    2. Relevant equations



    3. The attempt at a solution

    cos(3θ) = 0.85

    3θ = 31.79°

    θ = 10.6° (3 s.f)

    I have drawn my transformed cos curve, where the full wave completes after 120°, so there are 3 full cycles in my range.

    I often make silly mistakes and i'm not sure of the best method to check my results.

    Using the symmetry of the curve I have calculated that θ = 10.6°, 109.4°, 130.6°, 229.4°, 250.6°, 349.4°.

    So, how do I verify these?
     
  2. jcsd
  3. Nov 7, 2013 #2

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    For what quadrants is the cosine positive?
     
  4. Nov 7, 2013 #3
    1 and 4
     
  5. Nov 7, 2013 #4

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Which of your solutions meet this criteria?
     
  6. Nov 7, 2013 #5

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi BOAS! :smile:
    Easier if you write:

    cos(3θ) = 0.85

    3θ = 2nπ ± 31.79° :wink:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Solving Trig Equations In A Given Range
Loading...