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!

Trig cosx question

  1. May 14, 2012 #1
    1. The problem statement, all variables and given/known data

    solve 5sinx +12cosx =6.5 between 0 and 180 degrees

    2. Relevant equations



    3. The attempt at a solution

    i tried squaring both sides. (5sinx +12cosx)^2= (6.5)^2

    25sinx +60sinxcosx +60sinxcosx + 144cosx^2 =42.25
     
  2. jcsd
  3. May 14, 2012 #2
    Squaring isn't really a good idea since it might yield extraneous roots. Try writing the given expression as a single trigonometric ratio.

    Hint : try converting it into a form of sin(x+T)
     
    Last edited: May 14, 2012
  4. May 14, 2012 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Sine is always postive between 0 and 180 degrees so you can write that as [itex]5\sqrt{1- cos^2(x)}+ 12cos(x)= 6.5[/itex].

    Rewrite it as [itex]5\sqrt{1- cos^2(x)}= 6.5- 12 cos(x)[/itex] and square both sides.
     
  5. May 14, 2012 #4
    Or, you can divide equation by [itex]\sqrt{5^2+12^2} = 13[/itex], and you will have
    [itex]\frac{5}{13}\sin x + \frac{12}{13}\cos x = \frac{6.5}{13} = \frac{1}{2}[/itex]

    And you know that [itex]\cos \arccos \frac{5}{13} = \frac{5}{13}[/itex] and [itex]\sin \arccos \frac{5}{13} = \sqrt{1-\left(\frac{5}{13}\right)^2} = \frac{12}{13}[/itex]

    And then, use formula for [itex]\sin(x+y)[/itex]

    sorry for bad English
     
  6. May 14, 2012 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Excellent Engliosh, excellent mathematics!
     
  7. May 15, 2012 #6
    This is exactly what I was suggesting. :smile:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Trig cosx question
  1. Trig question (Replies: 4)

  2. Trig Question (Replies: 1)

  3. Trig question (Replies: 2)

  4. Trig question (Replies: 16)

Loading...