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!

Trig Question, Find x-intercepts

  1. Sep 2, 2012 #1
    1. The problem statement, all variables and given/known data

    List all x-intercepts for y= -5sin(4x+pi/3) On the interval [-pi/6, pi/2)



    2. Relevant equations

    I know that y=sin has x-intercepts at 0, pi, and 2pi on the interval of [0, 2pi] but when I try to solve it the same way here it doesn't really come out the same.


    3. The attempt at a solution

    This is how I tried to solve it,

    -pi/6 < 4x + pi/3 < pi/2 ----> I subtract pi/3 from both -pi/6 and pi/2

    = -3pi/6 < 4x < pi/6 ----> Then I divide 4 by both

    = -3pi/24 < x < pi / 24

    so the x-intercepts would be -3pi/24 (-pi/8) and pi/24 and the midpoint between those but I guess its wrong :(
     
  2. jcsd
  3. Sep 2, 2012 #2

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Hello dolpho. Welcome back to PF !

    You're told that [itex]\displaystyle -\frac{\pi}{6}\le x\le\frac{\pi}{2}\ .[/itex] Now find the interval on which [itex]\displaystyle 4x+\frac{\pi}{3}[/itex] then occurs.

    You have worked it out as if [itex]\displaystyle -\frac{\pi}{6}\le \left(4x+\frac{\pi}{3}\right)\le\frac{\pi}{2}\ .[/itex]
     
  4. Sep 2, 2012 #3
    Ahhh my mind is messed up on this problem!

    I worked it another way so that

    0= -5sin(4x + pi/3)

    -pi/3 = 4x

    -pi/12 = x

    So I think that part is right but what if I wanted to find more x-intercepts along the interval of -pi / 6 and pi/2?
     
  5. Sep 2, 2012 #4
    [itex]\Large period=\frac{2\pi}{b}[/itex]
    for the form:
    [itex]\large asin(bx-c)+d[/itex]
    so your b value is 4. There will be an x intercept every half-period.
     
  6. Sep 2, 2012 #5

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    You could work it out:

    [itex]\displaystyle -\frac{\pi}{6}\le x\le\frac{\pi}{2}\ [/itex]

    [itex]\displaystyle -\frac{4\pi}{6}\le 4x\le\frac{4\pi}{2}\ [/itex]

    [itex]\displaystyle -\frac{2\pi}{3}+\frac{\pi}{3}\le 4x+\frac{\pi}{3}\le2\pi+\frac{\pi}{3}\ [/itex]

    etc.
     
  7. Sep 2, 2012 #6
    Ok so I think I found the answer.

    0 = -5sin(4x+pi/3)

    -pi/3 = 4x

    -pi/12 = 1 x-int, Then I find out the period so, 2pi / 4 = pi/2

    Add pi/2 to -pi/12 = 5pi/12. Then find the midpoint between those so the x-intercepts would be

    -pi/12, pi/6 and 5pi/12

    Anyone get the same answers?
     
  8. Sep 3, 2012 #7

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Those are correct.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Trig Question, Find x-intercepts
  1. Finding x intercept (Replies: 7)

  2. Finding X Intercepts (Replies: 7)

Loading...