1. Not finding help here? Sign up for a free 30min 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!

Cos(A-B) vs sin(A+B) [acos(x) + bsin(x) question]

  1. Jun 27, 2015 #1
    1. The problem statement, all variables and given/known data
    I already solved the question but there was a question at the end just for thought I guess.

    Solve the equation 3 cosx + 4 sinx = 2, for values of X from 0 to 360, inclusive.

    Again I already solved it ,the thing that I am curious about is the question below in bold.

    " What advantage is there in using the formula for cos(A-B) , rather than that for sin(A+B) in the above question?"


    2. Relevant equations


    3. The attempt at a solution
    I don't see any advantages. But I am not entirely sure?
     
  2. jcsd
  3. Jun 27, 2015 #2

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    What steps did you follow when you solved it?
     
  4. Jun 27, 2015 #3
    cosycosx + sinysinx = constant

    Comparing this with
    3cosx + 4sinx = 2

    so
    (cosy)/3 = (siny)/4 that is tany = 4/3

    so y = 53.13
    and siny = 4/5 and cos y = 3/5 therefore

    3/5cosx + 4/5sinx = 2/5

    therefore cosxcosy +sinxsiny = 0.4

    cos(x-y) = 0.4
    x- 53.13 = 66.42 or 293.58
    so x = 119.6 and 346.7
     
  5. Jun 27, 2015 #4

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    So, that's the solution using cos(A - B).

    The solution using sin(A + B) must have sin(y)cos(x) + cos(y)sin(x) = constant .

    Giving tan(y) = 3/4, so that y ≈ 36.87° and sin(x + y) = sin(x + 36.87°) =0.4

    Thus x + 36.87° ≈ 23.58° or 156.42° , plus multiples of 360° for each .

    So, why is the cos(x-y) method easier to work with in this case?
     
  6. Jun 28, 2015 #5
    Hmm because the cos(x-y) gives the write answers? When I put the answers gotten from the sin(A+B) it doesn't satisfy the equation.
     
  7. Jun 28, 2015 #6

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    You will get the right numbers eventuality.
    x + 36.87° ≈ 23.58° gives -13.27° . Add 360° to that to get346.71° .

    So, what's the advantage/disadvantage?
     
  8. Jun 28, 2015 #7
    Oh , well all I can say is that the cos(A-B) has less steps.
     
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: Cos(A-B) vs sin(A+B) [acos(x) + bsin(x) question]
  1. Sin(x) + cos(x) (Replies: 4)

Loading...