Results 1 to 8 of 8

Math Help - Intersection - Solve Trig Equation

  1. #1
    Junior Member
    Joined
    Sep 2011
    Posts
    27

    Intersection - Solve Trig Equation

    Hi, in order to integrate this function between 0 and pi/6 I need to solve for the intersection points to find the limits of integration. However, I am totally lost on how to solve it.

    6cos(3x)-6sin(6x)=0

    Any help would be kindly appreciated.

    Thank you in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5

    Re: Intersection - Solve Trig Equation

    Quote Originally Posted by sjmiller View Post
    Hi, in order to integrate this function between 0 and 6 I need to solve forthe intersection points to find the limits of integration. However, I amtotally lost on how to solve it.

    6cos(3x)-6sin(6x)=0

    Any help would be kindly appreciated.

    Thank you in advance.
    The equation simplifies to cos(3x) - sin(6x) = 0.

    There are several options for solving this. One option - depending on your background - is to use the double angle formula sin(6x) = 2 sin(3x) cos(3x), substitute, factorise, use the null factor law, solve for x.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,130
    Thanks
    1012

    Re: Intersection - Solve Trig Equation

    Quote Originally Posted by sjmiller View Post
    Hi, in order to integrate this function between 0 and 6 I need to solve forthe intersection points to find the limits of integration. However, I amtotally lost on how to solve it.

    6cos(3x)-6sin(6x)=0

    Any help would be kindly appreciated.

    Thank you in advance.
    start by dividing by 6 ...

    \cos(3x) - sin(6x) = 0

    let t = 3x ...

    \cos(t) - \sin(2t) = 0

    \cos(t) - 2\sin(t)\cos(t) = 0

    \cos(t)[1 - 2\sin(t)] = 0

    \cos(t) = 0 ... \cos(3x) = 0

    \sin(t) = \frac{1}{2} ... \sin(3x) = \frac{1}{2}

    finish it ...
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Sep 2011
    Posts
    27

    Re: Intersection - Solve Trig Equation

    Hi, so it appears the answers are 1 and pi/6. But if this is the true set of solutions then how can the two functions intersect between 0 and pi/6 radians?

    I know this is a bit off topic but perhaps it will help you understand what i'm trying to get at.

    I need to find the area between the curves y=6cos(3x) and y=6sin(6x), x=0, x=pi/6... Does the compression factor 3 and 6 have an effect on their intersection in the given interval?

    I get the period has been compressed by these factors but I'm not sure how to go about finding the solution in that interval...
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,130
    Thanks
    1012

    Re: Intersection - Solve Trig Equation

    Quote Originally Posted by sjmiller View Post
    Hi, so it appears the answers are 1 and pi/6. But if this is the true set of solutions then how can the two functions intersect between 0 and pi/6 radians?

    I know this is a bit off topic but perhaps it will help you understand what i'm trying to get at.

    I need to find the area between the curves y=6cos(3x) and y=6sin(6x), x=0, x=pi/6... Does the compression factor 3 and 6 have an effect on their intersection in the given interval?

    I get the period has been compressed by these factors but I'm not sure how to go about finding the solution in that interval...
    this is what happens when one does not post the entire problem ...

    the graphs cross at x = \frac{\pi}{18} and x = \frac{\pi}{6} ... I'll leave it for you to figure out why and which curve is above the other in the intervals \left[0,\frac{\pi}{18}\right] and \left[\frac{\pi}{18} , \frac{\pi}{6}\right]
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Sep 2011
    Posts
    27

    Re: Intersection - Solve Trig Equation

    Thanks a lot for the help... Do you know of any good texts I can buy to decrease my lack of knowledge with trig functions. Were beginning trig integrals and I feel its going to end badly if I dont increase my knowledge.

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,130
    Thanks
    1012

    Re: Intersection - Solve Trig Equation

    you don't need a text ... go search on google. you'll find a veritable plethora of info on trig graphs and solving equations.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5

    Re: Intersection - Solve Trig Equation

    Quote Originally Posted by skeeter View Post
    you don't need a text ... go search on google. you'll find a veritable plethora of info on trig graphs and solving equations.
    The OP will also find a lot of info
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Compute Trig Function Values, Solve Trig Equation
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: September 8th 2011, 08:00 PM
  2. solve this trig equation
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: April 6th 2010, 05:42 PM
  3. solve trig equation help.
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: November 20th 2009, 07:11 AM
  4. How do I solve this trig equation??
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: November 16th 2009, 08:16 PM
  5. Solve this trig equation
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: September 18th 2009, 03:35 AM

Search Tags


/mathhelpforum @mathhelpforum